I don't think it is an invisible enemy because the health drain perfectly coordinates with my movement, so I guess it is a trap.
What about the orcs and the girl? Is this a buggy quest, or am I just not looking in the right place?
To see if the quest is indeed bugged, save your game then press [ or ]. That will teleport you through the several locations in the dungeon where the girl might be.
When you teleport, have a step backward, because you always get teleported on the quest object/NPC and you can't see it.
If you see that the girl is indeed in the dungeon, try to resist the urge completing the quest the cheater's way and reload your save game.
If she is not there, check your journal to see if your quest is still active or make sure you are in the right dungeon.
Otherwise, the girl is most likely invisible due to an evil bug. But failing a quest in Daggerfall doesn't change much. You'll still have an infinite number of quests to perform (But you'll always have the thought that you left an harmless girl to be eaten by orcs)