Yes, it should have a EEC-IV computer in it. Ford starting putting EEC Computers in cars in 1978. You may have an EEC-III, but I'm pretty sure Mustangs had EEC-IV by '85.
If it is an auto then yes it has an O2 sensor because the auto cars got CFI. If it is a manual it has a carb and has no O2 sensor but it does have a computer that is just an emmisions control box.