Hi Janice! The first thing I'll say is that I have NOT tried this BUT I know what I would try. I don't know how large your oil stains are but I would try a THIN coat of Dawn dish washing liquid and, depending on your carpet pile, rub it in either with a tooth brush or fingers (rubber gloves?). I'd let it sit for a few minutes then I'd start to rinse it out with clean water until the area doesn't suds any more.
I have never had Dawn fail on getting oil stains out of laundry; fresh and old dried on stains. I hope this helps. I'm sure there will be a lot of other great ideas from the wonderful members of this site.