I'm not really sure what you could do for her oily fur. The only thing that popped into my head was getting some waterless shampoo. I've never used it before, so I really don't know all about it. I've seen it at pet stores before though. I think it's just a powdery type substance & you comb it through their fur.
Mabel's hair used to get like that... I switched cat foods and it cleared up. Even though her coat seems oily, you might find that adding something to her diet with some fat in it will help.