I've got a bunch of Giant Toes that I can't get rid of...it insists they're quest items. But I don't think I have such a quest. Can I start it somewhere so I can get rid of them?
They are used for the "Hangover" quest which starts with a drinking competition in which you black out and destroy a temple (see this question if you need help). One of the items needed to repair the staff is a Giant's Toe.
Skyrim has the annoying functionality that sometimes regular items can be quest items (Giant's Toes, Amulets of Talos), but they stack with their non-quest item selves, and you can't separate them.
To answer your question, Sanguine's Daedric Quest involves a quest-item Giant's toe. (See Uhh... I got drunk and trashed a temple. How do I pick up the mess?)