Okay, so I know this sounds like a joke, but it's not. I am 100% serious. So my world has this kind of... squirrel expy, that is somehow intelligent enough to use weapons + have some sort of society. Otherwise they're basically your average red squirrel (but slightly longer and chubbier). I was thinking like some sort of spear or blade held in the mouth, but what are you guys' thoughts?
Assumption: your squirrels have the same hands and roughly the same body that earth squirrels have.
In order to choose a weapon, it is important to know (and I keep repeating myself there everytime I answer a weapon related question): what are the conditions they are used in? What opponent do you have? What armor do they wear?
First off, squirrels do have kind of opposable thumbs, but they don't use them the way we do. But I think that if your squirrels are of higher intelligence, they may use them or quickly develop them to full effect. Since opposable thumbs are a huge evolutionary advantage, especially for an intelligent being, I assume your squirrels have them.
Squirrels hunting prey
If your squirrel is hunting other animals, for example to gather fur, leather, bones, sinews fat etc., they require typical hunting weapons. A doubt a squirrel can possibly generate enough kinetic energy to seriously injure bigger creatures like deer or bears. Even wild boars will be a no-go. But they could kill smaller prey like bunnies or mice. For that, they'd either go trapping, or hunting with small bow+arrow or by flushing them out of their burrows. Since none of these animals can fight back efficiently, I think smaller weapons like axes and knives (flintknapped?) would do. They also allow to enter the tight burrows, while a long spear would be a hindrance.
Squirrels defending against predators
In order to defend against a predator, you need to do one thing: don't get eaten. How do you not get eaten? Especially if you are a frail little squirrel? You stay the heck out of reach. So all our defensive weapons will be long and of long range. But, even with a long spear, a squirrel probably can't defend against a cat or a wolf. The animals are just too huge, and if you don't hit a vital point (eye, nose), their first attack will kill or maim you. Even if you do hit an eye with your spear and somehow kill a pouncing wolf, the heavy body might still crush you. So melee weapons are completely out. Also, while holding a weapon, you can't climb. And fleeing is probably the best you can do.
So, vs. predators my best guess would be: escape to a tree, warn your friends. While the predator chases you, your friends make ready. If you reach safety on top of a tree, all is good. But if the predator tries to chase you or corners you, your friends neet to help. And I think only ranged weapons can help you here. And especially the sling might be super useful here. Slings can be made from cloth, and are therefore easy to store and carry while climbing. You can always have a sling with you for self defense, while a bow is a hinrance, and takes longer to make ready (you can't always have a string on your bow). Guards might go for bows or throwing spears (if thrown down from a tree, they might develop some power), but the common squirrel will carry a sling. This way you might chase predators off your tree.
The main cities and outposts will probably be secured by walls of spikes pointing downward the tree trunk, making it harder to climb it for bigger creatures. In these stationary locations, your squirrels might also store huge nets, that they could throw down on climbing intruders, catching them and potentially killing them during the fall.
Squirrels fighting squirrels
Since squirrels are fast and agile, but rather weak, I assume they do not wear significant armor. Maybe an occasional chestplate made from bark, since bark is relatively lightweight. If fighting another squirrel, you'll need to keep a balance between mobility and armament. If you use your hands for fighting, you can't run and climb. So I think one-handed weapons will prevail. And against unarmored opponents, weapons like the rapier and light sabres proved most effective in our history. A rapier could be made out of cactus spikes or even wood, if you don't have metalworking. Sabres could actually be flintknapped as a whole. Or you make swords like the macuahuitl, that would be rather heavy and probably one-and-a-half-handed, but a hit will END every squirrel.
Or go for the lulz
if technology is not that much of a thing, and you just want to go for the funny ideas, try exploding nuts (thrown with slings), hand crossbows, flintlock pistols, or, most importantly: spears with detonating tips, used by squirrels with impressive mustaches, that ride on giant ferrets, while wearing Pickelhauben, monocles and speaking with a german accent...
A squirrel is sufficient weapon in its own right. In violation of normal StackExchange protocol, I won't summarise the link because spoilers, and, well, just read it and it'll improve your day, OK? :)
In case anyone doubts this testimony though, the Daily Mail has headcam evidence of a squirrel getting in someone's face for no particular reason.
More seriously, I wouldn't rate throwing weapons because they don't have the bodymass to launch anything that's more than an annoyance. Acorns might sting, but they're not going to knock you out.
Thing is though that anything they carry will slow them down, and impede both attack and escape. A more natural approach would be a school of martial arts based on assessing the weak points of your opponent (particularly ways into any armour) to get right in close and do maximum damage when they get there. It's hard to stab or shoot a squirrel if it's running round the inside of your body armour! And then of course they're trained for where to find major nerve clusters, tendons, exposed veins/arteries, all that good stuff which will incapacitate a victim in very little time with nothing more than sharp claws and teeth.
I see them using tons of poisons, in order to fight much larger opponents. Find the right plants, mush it up, and use some sort of spear to deliver it, thrown or stabbed. Maybe a ballista if they were organised enough.
It's a practical way they might take down larger prey, be that prey a fox or a human. The kind of poisons you get in squirrel territory might not be on the "poison arrow frog" end of things, so they'd likely attack, then track, if they need to retrieve anything of the target. They would also need use of fire and perhaps pottery in order to have a way of reducing the poisons.
They could potentially be using trapeze-like skills, and swinging attacks on rope, to deliver poisons, something like a very low-tech Attack on Titan.
If you were using plants available in the UK or Ireland, you get the bonus of cool names for the poisons as well.
Interesting answer from Andreas, but I'd take issue with one of his points
Since squirrels are fast and agile, but rather weak
For their size, they are anything but weak. I mean an animal that can dart up a tree as fast as one can blink can hardly be said to be weak!
I was feeding a tame squirrel in Hyde Park (London), and having run out of nuts I held out my empty hand loosely clenched. This squirrel managed to haul open my fist, with one arm on my thumb and the other hooked round my index finger, with amazing strength (although I didn't put up much resistance). On finding my hand empty, it gave me a token nip, which I'm sure could have been much harder had it wished!
Getting to the point, I think a squirrel would likely make more use of its back legs. Perhaps it could fit a sharp scythe-like blade to each back ankle and thus be able to fight like a cockerel leaping up and slashing at its opponent, and likely holding a couple of shields in its front paws, to protect itself from a similarly armed opponent.
A squirrel could wield quite a large bow and arrow by rolling on its back and bracing the bow on its back legs and hauling back and releasing the bow string with its front arms. If it fired a poisoned arrow and then scampered off and kept out of the way until its prey succumbed, it could kill a sizeable animal.
Perhaps it could make good use of its large incisors by attaching round its head an armoured helmet with an artificial set of external teeth-like blades or spikes operated via a spring-loaded caliper arrangement by its real teeth inside, if that makes sense. Again, if the external blades were poisoned, it could bring down a larger opponent, although with this contraption close to its mouth and probably breathing heavily it would have to be careful not to ingest the poison!
Also, let's not forget its large tail. It could attach a blade to that and swish it round, perhaps as a defensive move while being closely chased by an opponent.
Definitely a Garrote. Just look at how nimble squirrels are, how easily they are able to navigate around tree trunks; one could easily trail a strong cord and run around prey to do any number of things, including tripping them up, tying together their limbs, muzzling, and even strangulating them.
They could work if groups of squirrels work together to “net up” a large animal, darting in and back to a safe distance.
Just pulling a cord (held in the jaws) avoids all the issues of weilding weapons in the paws or having the body mass behind strong blows.
Swords, needles, bees, axes, just about anything from Redwall or Mouseguard.
But with a realistic squirrel, that is harder to say. They do have opposable digits, but I'm not sure how they'd be with gripped weapons. A spear in the mouth will, unfortunately, be useless anyway I can conceive of it.
They could probably throw stuff, squirrels love throwing things. That does give me the impression that, if necessary and intelligent, they could learn to fight with hand weapons. They could walk with three legs, having a sword in the right forepaw, or they could learn to walk bipedal.
Of course, squirrels are so terribly fast, they could run on all fours, grab and bite onto the enemy, then quickly pull out a knife and start cutting, changing position and repeating as needed. Against enemy squirrels, it's be a lightning quick pounce, then the knives come out. If the knives can also be thrown, bonus.
Though spears are a real possibility, in squirrel vs. squirrel combat (choosing reach and killing power over four-legged mobility). They might even be able to load a crossbow if they used their teeth or something.
Traps, ropes, wires and poison needles; maybe in some kind of spike helmets.
I think that due to the size and structure of a squirrel it is best to let them move naturally in CQC.
Traps are static so they are kind of trivial as there is no need to specialize them for squirrels.
Poison needles can kill. With some kind of a helmets the squirrels can move naturally and swarm over armored enemies and get to weak spots. Traps can help to immobilize the enemy as do ropes and wires.
The squirrels can use ropes and wires in groups. Due to their low mass they could quickly make some kind of trap like mechanisms to utilize counterweights. Nothing more than some basic like a rope tied to a stone dropped over a branch.
Cutting wire will be pretty nasty against unarmored enemy, even without counterweight.
One, utilize dangerous animals. Enrage a boar into chasing you, then run through a group of humans. Encourage bees to move to strategic locations, then cut whatever is supporting their hive on top of invaders's heads. Train a bear to not think of squirrels as food, then live near its den. Have pet skunks. The world is full of creatures that can do far more damage than a squirrel can.
Two, guerilla warfare and crazy revenge. In a straight fight, a squirrel probably loses. But they'd be great at sneaking around, hearing secrets, lighting stuff on fire, slitting throats in the night. Having a culture where you let people know that you will wreck their shit if they mess with you is a pretty effective deterrent, even if the other side knows that they would win in a straight fight.
Edit: Today, I learned that squirrels are omnivorous: Squirrel chomping on a mouse (Video).
Given squirrels' masterful ability to overcome bird feeder defenses through their tremendous agility, dexterity, tenacity, and puzzle solving skills, I'd say you've got a good argument for rather Rube Goldbergish weapon systems. Given their proclivity for heights, I'd say that gravity fed projectiles and castle-defense measures mounted on Oak trees would be their MO. Also, if they have any amount of breathing room to cultivate things on this planet, they would be planting oak orchards and protecting the oldest, most productive trees and would build up multi-clan societies as tree to tree cities. They are already rather family and clan oriented and would quickly form larger scale mutually advantageous societies allowing them to share information across distances and circulate rare/specialty goods; this would allow for the development of more advanced weapons. As the rats of the trees, they're going to be hardy and fierce, however, I would expect their methods of war to be conservative and opportunistic since most rodents have strong predator-evasion instincts (hence the ranged weapons from on high).
And might I agree with my fellow thread poster... "rabid berserker squirrels". ... ohhellyeah
Having observed squirrels, and watching them move from tree to tree.
It seems obvious that they would prefere ranged weapons.
The only good reason to be on ground level is to find fallen food.
Nature provided them with high agility and excellent reflexes.
(just look up that youtube video of a squirrel stealing food from a cat, and you know how badass they can be).
Since they probably want to keep moving in the trees, it wouldn't be a weapon that they have to carry by paw.
So something they can carry on their back.
And not something overly heavy that would mess up their balance while jumping branches.
A possible solution for those requirements?
A pawheld catapult to shoot explosive acorns.
Just to add on - Squirrels have extremely sharp claws. The reason they're not considered good pets is that they'll cut through your flesh pretty easily just by innocently trying to climb up your leg.
Ask any veterinarian that's cared for a squirrel before releasing it back into the wild: They're cute, but their claws and teeth are extremely painful.
If the squirrel civilization has metallurgy -- or even basic stone knapping, if they can do it precisely enough on a small scale -- they could get Wolverine-style claw extensions. (See: Guardians of Ga'Hoole series, for owls.)
This option gets around the issues with having to hold something in mouth or claw, by simply extending claws. Note, however, that the claws would need to be very strong and well developed, or alternatively not interfere with the process of walking or climbing by attaching above the hooked section.
Arguably, this doesn't necessarily grant much of an advantage to the squirrel, since their claws are already so sharp. Might be decent for stopping predators, though.
Having had a squirrel drop a slice of bread on me, it's pretty obvious...
They ambush and drop something heavy from high overhead. All you need is some good pine trees that produce large pine cones. The coulter pine (thanks to DJohnM in comments) would be a good candidate. They can weigh 10 kg. Now imagine that the squirrels are dropping these from 10 meters high. That's a 10 kg weight going 50 km/hr at impact. https://www.angio.net/personal/climb/speed.html
Give your world slightly larger pine cones or slightly larger trees, and no one survives a journey into the Squirrel Wood.
Has everyone forgotten the scariest weapon that small mammals wield IRL?
Granted squirrels rarely carry rabies, but woodchucks accounted for 86% of the 368 cases of rabies among rodents reported to CDC. It wouldn't be a stretch to have rabid berserker squirrels.
Two things not mentioned yet (especially useful when combined):
Mass group attacks. This would require behavioral change only, and since they have become intelligent, that's just a decision to take. With their agility, claws and teeth you do not want to face 200 squirrels attacking you.
Use sand, it's widely available and you don't have to carry or maintain it. That same number of animals thowing a barrage of sand in your eyes, nose and mouth is again something to avoid.