I think you can rule out any weapons that are designed to be swung (either side to side or overhead) repeatedly, as without being braced against the ground (or a rider in a saddle of a larger creature) it would be difficult to control their own bodies using such weapons (consider the effects of throwing even a light ball quickly while playing water polo, then adapt to trying to maintain position in mid air using wings at the same time as offsetting the swings of your weapon). Besides going into melee while still trying to fly just above the ground near your opponent would seem to give up any advantage flying gave them anyway.
That leaves two options I can think of, with missiles fired at range being the first - and direct fire missiles of any sort also seem like a bad idea as well (whether bows or firearms of some sort) - trying to fly in one spot while aiming at a remote target and keep your attitude is going to make for very low accuracy (which only works if there is going to be a lot of them to fire at once). I guess dropping something (maybe explosive or burning) would work though, although the mass and amount of times they can attack would then be limited by how much ammunition they could reasonably carry, which presumably would be quite low - think of the trouble larger birds have getting off the ground, so adding lots more mass is going to be hard to justify.
The other possibility is to parallel medieval knights or cavalry and use the mobility and speed of their flying to impale their enemies with something like a lance or spear as they "charge", or maybe something like a sabre used to cut down on enemies heads and necks as they fly past - this has the advantage (for your requirement) that it is mostly a cutting weapon because you don't want your weapon to get stuck in an enemy as you charge past, although they usually also have a sharp point for if you get bogged down and want to do damage as far as you and your weapon can reach, which may not be as much of an issue for these Angels with their even greater range of mobility.
So I could see either Angels with a lance charging at a something like a phalanx (or something along similar lines with shields and spears) - they can't attack too vertically or the Angel will crash into the ground as they follow through from the attack, but they would be able to change the direction of attack fairly easily, although still needing enough space/time after turning to get back up to speed to make the most of it. Of course solid hits are mostly going to be fatal, except limbs which would be more disabling but hard to do deliberately/repeatedly.
Alternatively with a sabre or similar weapon I could see them flying past repeatedly slashing and cutting each time, and as they are likely to stay around head height (or maybe slightly higher) and strike down on their opponent as they pass, most hits would be to the face, arms and neck.
Combating this would probably be spears again (at least for any melee fighters, maybe protecting archers to shoot at them in the air or as they approach) - you certainly want some range on your weapon to reach the opponent as they fly past, the shorter the weapon you wield, the smaller the window of opportunity to strike at them. Bladed polearms are unlikely to be useful as they are difficult to swing from side to side (while maintaining balance) - usually you are chopping downwards on the enemy (axe like), or using it to keep them at range while using either a pointed end to do the damage, or something like a hook to drag them down and remove the enemies mobility.
Defenders with swords would at least be able to protect themselves reasonably well, but counterattacking would be difficult as the Angel would likely be past them by the time they can strike, although maybe they could damage the wings as they go past, especially if they can parry the sabre in a way that allows them to immediately carry on into an attack as part of the same movement.
Overall I would try to analogize the Angels to mounted soldiers - weapons to take advantage of their mobility relative to their opponents, and tactics to avoid losing or wasting this advantage are going to make the most sense.