Radiator sludge oil in the radiator, but no water in the oil.

Hello Todd, sitting here thinking about it only 2 things comes to mind. First question is it is an automatic. If so then your transmission oil cooler inside the radiator has a leak which in turn it leaking transmission fluid into the radiator. So if it is the transmission do you see any red gunk in the radiator or the water. Now same process if it is motor oil if it is a manual transmission. These new vehicle have motor oil flowing through the radiator to cool off the motor oil also known as the oil cooler. 9 times out of ten all you have to do is buy a new radiator or remove the metal or rubber lines running to the radiator and splice them together with high pressure hose. Which I recommend power steering return 3/8 hose, tough stuff. Just slide the rubber hose over the tube and clamp it down tight with a hose clamp and give it a whirl. But first I recommend you flushing the radiator. Good luck.