My son's car had his problem---bad. This is what we did. Either way, do the standard tests for a head gasket just to be sure. Engine oil pressure, and the Trans fluid pressure is higher than the water pressure so the oil/fluid will go into the radiator, not the other way around--unless it is a bad leak.
Need to first verify it is oil in there and not just crap. Empty the overflow into a clear container. Both the water and the "oil." Shake it up and let it sit. As you know, the oil will settle to the top so just let it sit for a bit. Oil on top, crap on the bottom. Next see if it is engine oil or trans fluid. You would think you would be going thru a lot of whatever it is, but a little will go a long way. The redish color is the trans fluid, and black is oil. If in doubt, have dirty oil in the engine and then change it. See if the color changes. My mechanic friend tried his hydrocarbon test but no luck. No bubbles in the radiator so we could not figure out what it was. Figured it was the head gasket. He went to replace it, and found a couple of loose head bolts-- Go figure. Tightened them up and all is OK.
Good luck, and let us know what you find. Just FYI, when we disassembled my 472, we found the beginnings of a head gasket leak. No signs, but we could see a trail where the water was creeping around the head.