Before you go to far, I would drain all the coolant out. Then, get a good radiator flush and wash the coolant system out good. Maybe even doo it twice. Then fill it up with water only and run it a while to see if oil shows back up. If the oil cooler has been disconnected already, that could be the culprit and the previous owner my have disconnected it because it was leaking, but did not get the oil cleaned out of the coolant system. I had a Ford TW-30 Tractor back in the 80’s on the farm that the oil cooler went bad and filled the coolant system up with oil. Took quite a lot of cleaning to get it all out, then put a new cooler on. Remember that for oil to get into the coolant, it has to be a leak where the oil is under pressure.