Errrm, some other tips, with a double post and all. Non-RNG or class dependant (sort of)
Gift dropping in AoB and AoMr (especially on UV):
It might seem like it's playing the system, but Line-of-sight in DoomRL is a bit screwy. I can't say if all advice here represents the current state of play, some of it is from previous versions.
I'm not sure if it's still the case, but HKs and Barons used to pick up ammo. It used to be worthwhile to give them a stack of shells, without any problems. No gain for them, but a chainsaw to the face or a hail of pistol shots for their troubles. One turn of "duh? SHELLS. MINE!" was great in any challenge mode. The AI has changed. Do they still do this?
Wear some armour early for the simple point of having it damaged whilst you kill things. You will take some damage early on anyway. In AoB, keep your inital blue perfect, or at ~24%. Greens are great too. Remember to stock up on busted armour. In AoB and AoMr you only have a few viable weapons. Therefore you have a couple of slots for gift drops. One is never enough. A former will die easily, but if you're assailed by HKs and formers early, two is great. Drop one of them back from a doorway a square, then another the next square back from that. Once one is grabbed, the next is still a noticeable gift-drop, thus funneling formers and surrounding HKs to the same area. Since you'll be standing beside said doorway, anything near will go into melee mode.
The reverse of this: Sometimes you want wandering enemies to just wander off. They haven't seen you, but one of their friends has noticed your gift. Specifically for AoMr, 1-on-1 is fine. Two gifts can make a horde-group that you don't want to deal with.
Strategic map control:
Close the f'ing doors. It's important. There's a lot of things that don't open doors. The things that do make sound when they open the doors. Close the doors. You're a space marine. Clean each area and seal it behind you. If you open up the entire level and wonder why something you didn't see on the first run through hits you a couple of times, it's your fault. You didn't close the doors.
Barrels of acid/lava. If you don't specifically need them now, group them the best you are able to in that room, near a closed door or at a nice area to shoot/melee into preferably (from another doorway or choke-point). Drop a gift beside them. You now have a small area with bonus damage. Drop 3 gifts if you have to. You might get a gathering of enemies that need bonus damage done to them. Not all challenges let you use rockets, all of them let you use barrels.
Barrel corner shoot. Push a barrel near a corner/wall-vision-stop. Drop a gift near it. Shoot/knife-throw the barrel to death after a few turns of waiting. AoE corner shooting in action.
Enemies are dumb. They either won't walk anywhere near acid/lava, will walk/fly right through it, or will take plenty of damage wandering through it. Terrain/walls/rivers and barrel-pops are your friend. Honestly, even when you're not taking much notice, you're better at dealing with this sort of stuff than the hellspawn you'll face.
Edit: I'm a bit of a grammar-nazi on myself. The internet's international, so I vaguely try and make my posts more understandable. Sometimes.