As I stated in my comment, it is hard to say without far more information about them. Lets assume a few facts that seem most probable.
they lack numbers, on the presumption that if there were many we would know about them
They are very good at hiding themselves from humans
They either can-not or do not utilize technology to the degree we do, or they would be a bit hypocritical complaining about us
They are intelligent as regular humans, or they wouldn't make as interesting a story.
Going with this I would say a direct fight would be hopeless. We could bomb any large collection or armies of them, or role in a tank and squash them. Our power is not in the size or strength of a regular human, but in massive and expensive weapons of war. If they have only 'some' magic I'm assuming you don't expect them to be able to bring the kind of magical BOOM that could take out a tank? if they can't then their only hope in a direct war would be to use our own weapons against us. However, we already own them, they would have a hard time getting them from us; and we still are the only ones with the ability to manufacture them. Plus, we still have a major number advantage.
Some have mentioned allies, but I don't think this will help much. Unless your allies also own tanks and fighter jets their worthless. In modern era it is our technology and weapons that decide direct wars. A hundred men with small arms can be destroyed by just one tank. Sure getting allies is always good, but unless you can ally yourself with entire governments it's not going to come close to evening the odds. And if you could ally yourself with large governments then this becomes a war of humans against humans more then anything. Plus, if your goal is destroy all humans who use destructive technology allying yourself with the group that has the most destructive technology (weapons) seems kind of hypocritical.
However, an asymmetric war is still quite possible. Gorilla warfare has proven capable of defeating far stronger militaries in the past. In this case your mythical creatures already have a massive trump card; they can hide! I don't know how they hide, but they do it well enough that we don't even know of their existence. Whatever tricks or magic they use, it's powerful. The most important ability of an guerilla is to be able to disappear after an attack, being able to do it with untraceable magic is huge.
How effective a gorilla war would be depends on many things, but most notably just how good they are at hiding and how well the can move while hidden. If they could, for instance, appear in the middle of a boot camp, have the unicorns stampede over the trainees, and then disappear with a finger snap to be untraceable....that would be ungodly powerful. Now every single location where any military officer is would have to be guarded with weapons 24/7, or faeries can appear and kill you. Your tanks and aircraft mean nothing, because you don't have anything to bomb, and your enemy will have disappeared before you can get to your weapons of war. This takes the battle down to mythical creatures against small arms, as they most lethal weapon that can be available in response to an unprovoked lightning attack, which is more effective.
Taking it further you said fairies were tiny, and that's powerful. Imagine the ability to appear in the home of an officer and assassinate him with a poison or some magical spell. or sneak in and just listen to their plans. For that matter a war of terror that worked simply by assassinating any who stand up to lead others against you would pretty quickly cripple any military by removing their leadership, and making everyone afraid to step up to do so.
How deadly they are now depends on how well they can hide, how well humans can adapt to it (will we learn ways to stop their magic, create magic-radar etc?), and how evil they are and what atrocities they are willing to commit. I need to know far more about them and their abilities to say further, but I will say that one way or another this must be a gurella war. If they amass in any number tanks and fighters destroy them.
Of course this assumes it goes to war. If your mythical beings are willing to reveal themselves they can do far more then fight a war. Their mere presence would change how humans look at them. If they tell us their suffering extensively due to some environmental damage were doing odds are we will work to stop that damage; humans aren't monsters, and once we have a face to place with the harm we do we tend to try to stop it. Just showing up and asking us to work to help avoid hurting them would be quite effective, not foolproof, but still powerful; especially since our culture would be so fascinated by them that we would listen raptly to them and worry about their plight to a disproportionate degree; we could ignore the deaths of thousands of humans to hunger to try to prevent the death of hundred of pixies to pollution because the starving humans are a faceless number, whereas the pixies are fascinating and our interest in them causes us to see their suffering in a way we don't with the boring starving humans.
If they were willing to teach us things they know, or offer their magic to us (maybe heal our sick, magic healing is pretty common in myths, and general far more effective then our hospitals), they would have further bargaining chips. They have many non-lethal avenues to peruse to get what they need.
It seems unlikely that a species would go from complete hiding to homicidal killing spree. There has to be a middle ground, of protesting and demanding we stop. A war risk their own lives, and kills countless humans if it is to win; and risks us using weapons that would further devastate the enviroment. I can't see a species so blood thirsty as to pursue such a lethal stance due to human ignorance of their plight managing to hide and ignore us for so long.