can oil get into the antifreeze?

Yes, if the head gasket is leaking and needs replaced, or a cooler line failure.

When I was at the dealership there only a couple reasons why oil got into the cooling system. 1st -- what type of oil in in the coolant ? Engine oil or transmission oil ? * if transmission oil , it's probably a leaking transmission cooler which is located inside the radiator. * if engine oil, it could come from a couple different places , 1, if equipped with and engine oil cooler could be Leaking from the engine oil passages to the coolant passages ( the engine oil cooler has coolant running through it) 2nd -- the other source would be the lower intake manifold gaskets leaking and allowing oil and coolant to cross contaminate ( this is of course if your vehicle is equipped with the 3.1 L engine) More importantly you gotta remember that the cooling system has to be thoroughly flushed out and usually have to replace replace the resivour tank and quite possibly all of the cooling system hoses depending on current condition.