If the oil didn't work, try WD-40. It takes the sticky residue left from price stickers and removes most oily stains. (If there is a film from the WD-40, my Dawn hand dishwashing liquid takes it right off.)
Once, we had been out of the house for quite a while; and our old recue mutt, who has never chewed anything since she was a puppy, ate a tube of bright red lipstick (used by my daughter for dance performances) and proceeded to vomit it all over our grey living room rug. I tried everything I could think of to get those marks out and nothing worked-- it looked like a murder scene! Finally I sprayed them with WD-40 and it worked like a charm.