Is this an auto trans? If so, the auto trans cooler/heat exchanger inside the radiator may have split. Check the auto trans fluid inside the trans for traces of water too (just incase). If it has split, you have 2 options: replacement radiator, or block off the stock trans cooler outlets by linking with a piece of hose and run an external cooler instead.
You can buy bottles of cooling system oil remover (500ml from memory) which you add to the cooling system to break down the oil and flush it away. Works really well!
If none of this applies to you, please disregard