I got a miscellaneous quest in Solitude to collect and deliver Roggvirs amulet of talos, but I already had that in my inventory and the quest will not complete and I can't drop it as it's a quest item.
Does anyone know how it can be completed or the cheat codes to drop the amulet and/or end the quest.

What platform do you play on? There are potential ways to fix it if you're on pc:

http://www.uesp.net/wiki/Skyrim:Return_to_Grace