So, my character has a curious issue. Things just magically wind up in his pockets while exploring manors or dungeons. Well, while exploring the Jarl of the graveyard city's manor, I found an 'Ancient Nord Necklace'. My question is, can I just sell it, or does it play a part in a quest? I ask because UESP provides no info on the item, yet I've never seen another like it, so I'm unsure if it's needed or not.

If you don't want it, you can sell it... no quest.

http://elderscrolls.wikia.com/wiki/Ancient_Nord_Amulet Since it's not tied to any quest you can sell it safely.

If it's a quest item, you can't drop it or sell it. In some cases not even after the quest is finished...