There is a pawn shop near your heaven in Santa Monica for a start, and as far as I remember there is some kind of shop in every district, I can't recall all of their whereabouts exactly.
I've been to the pawn shop and to Fat Larry, and I go into inventory, click on the item I want to sell and it says "can't equip". How do I hand it over? Dropping it doesn't work, either.
This almost got me too. You have to talk to the guys, and tell them you want to *buy* stuff. (Yeah, I know you want to *sell* stuff. It doesn't make any sense to me either.) Then when you get on the buy screen, just do the opposite to sell your stuff.