If a monster beats a hero in a battle with more than 2 physical damage, can they steal some of their items/omens? And what will the monster do with them, if they can do that, can they use them normally?
No, unless the specific haunt says otherwise, monsters can never carry items.
From the rulebook (first edition quote; though this did not change between editions):
Monsters can’t carry items (unless the haunt says otherwise).