How do you remove oil from cooling system?

There is no option but to completely drain the cooling system, then flush it through with a cleaning agent- special compounds exist for getting rid of oil contamination in the cooling system, you will need to consult your nearest auto spares & supplies store to find out which one they recommend. Once this has been done, flush the system through with clean water to remove any residue before re-filling and re-sealing; remember also to add the necessary amount of anti-freeze if this is necessary.