Okay, I feel like I'm going crazy, but the battle in the Slums with 4 Trolls and 2 Ogres is ridiculous. The troll hit points are insane, and they regen every round! Also, I get that trolls in AD&D will resurrect after death if not killed by fire, but you can't even kill them like that from what I can find out. I tested by killing them with Flasks of Oil and Burning Hands, and neither keeps them dead. Is this known, or is it random or something? I am scared to even keep playing if I run into any other trolls later on that I will get stuck on.
This is a notoriously difficult battle. It's not just you, it's extremely hard. It's by far the most difficult battle in the game in my opinion (given your party strength at the time you're most likely to encounter it). You are correct that burning doesn't work the way it is supposed to, it's a lapse in the game.
Protip: If one of your characters is standing on a space where the troll was when it died, it won't be able to come back to life.
There are a couple of strategies you can try:
1) Come back to this fight later when your characters are at least level 3 (This is what I personally always do).
2) Hire some NPC fighters in the adventurer's guild in Phlan, and equip them with bows and arrows.