Could be you have a bad chamber in the radiator that separate the coolant, as the oil passes thru a chamber in the radiator it has gotten thin and perhaps split, leaks over into radiator. Check to see if you have water bubbles on your dip stick, if so you may have a blown head gasket as well. and in turn oil and water is being recirculated thru engine block and back in the radiator.Why is there oil in my honda accord radiator?
if engine has over heated it is most likely a head gasketWhy is there oil in my honda accord radiator?
If the car has an automatic transmission the radiator is probably bad, the trans fluid is cooled in the lower part of the radiator so its possible for trans oil and coolant to mix if there is an internal crack, get this fixed asap.
it could also be a blown headgasket which you can have a mechanic run a test to verify, or buy a tester yourself.
Id start with the more likely (and cheaper) radiator and replace the coolant and trans fluid if it is.