Sorry to have to say it, but that looks toasted to me. Once some of the windings over heat and they loose their insulated coating, they short together and the transformer is no longer fit for service. Once you get burning and especially smoke coming from a transformer its usually a right off.
Hopefully someone here has a spare and can help you out. If you do find a replacement, make sure you test the circuits immediately after the transformer for shorts. You don't want to fry the replacment.
Good luck, I feel sorry for you in this situation.
