Are there any quests in the game that will actually remove these items from the game? I did teh quest where the body was indentified, but it's still in my backpack. If there isn't any more use for it I'll just drop it.

Yes, the dead girl is required to continue the main storyline in act 3, the dagger pieces are required to continue the main storyline in act 1. Both will be automatically removed from inventory upon completion of that stage in the main storyline. If you would prefer to drop it, be sure to drop it somewhere centrally located like the town square or your faction's building where they can be easily accessed to pickup for use later on.

Act 3....really... I did read that somehwere but I thought it was a typo for act 1 :).
I dropped her back in her grave at the Graveyard, to see if anything would happen. It didn't of course.

You don't have to carry the body around. Just leave it somewhere and fetch it when you need it in act 3.