Apparantly if you grab the executed guy's amulet of talos in solitude before getting the quest to grab it it makes all your amulets of talos quest items which cannot be sold or dropped (although they can be equipped).

I'm on the PC, is there any way to fix this issue via the console?

Try one of the console commands in the Bugs section of http://www.uesp.net/wiki/Skyrim:Return_to_Grace#Bugs

Unoffical Skyrim Patch.

This.
The Talos Amulet (and lots of other issues) were all fixed ages ago...
PC players need the Unofficial patches and BOSS - they are considered essentials.