If your cat is willing you should try to give him a bath using shampoo that you can find at your local pet store. You will need a soap based product to break down the mineral oil as it will cling to the hair and eventually get matted and dirty. If your cat is unwilling to go into the bath, you may want to dry a dry wash that you can also get at the pet store, but will be a bit less effective.
Sunlight dish soap. If it's good enough for the water fowl messed up by the oil spill then I would imagine it would work just as well in your case. Just rinse thoroughly so they don't ingest it when they lick their coat dry afterwards.