You have to sell the loot to fences. Only certain merchants will buy stolen goods, and almost all of them are part of the Thieves Guild and will not barter with you if you aren't part of the guild. There is, however, a merchant who will buy any stolen goods regardless of your factions. Manheim Maulhand, the owner of the Inn of Ill Omen, south of the Imperial City and north along the road from Bravil.