The best way to do this is actually with more oil. Vegetable oil or mineral oil or butter or olive oil or even peanut butter etc. Rub it into the oily area until the whole area is well blended then wash the cat with a cat shampoo or you can in a pinch use Blue Dawn detergent or Murphy's Oil soap to wash the area.
If some of the oil remains (this also works for tar or pine tar) repeat the process.
Hope this helps you!