I'm using just water, cause idk what is safe to use. Also iv just done the head gasket and all tq'ed down.. The only thing I can see, is the oil cooler.
You might want to pull the radiator and fill it with a de-greaser type solution, let that soak a while then flush. It could be too clogged though. I know radiator shops can take them apart and clean them out but it may not be worth it... you might need a new radiator. Realize that if you add water to the top of the cooling system (the tank) and if the thermostat is closed, you have to pretty much fill the hole engine block to the top then it starts flowing into the radiator, which means you will need at least a gallon of water. No, you don't need to drain the oil, you will just lose whatever oil is in the filter (maybe a quart or less) but if you think coolant has gone into the oil (if the oil like chocolate milk) then you need to change it ASAP. I would change it just to be sure, but only once you have fixed the oil/coolant mixing problem.