Can the stains be washed out with a normal washing machine?
Like most stains, it really depends on the fabric, the colour and how long you've let it sit for before washing. Personally, I have a cotton sheet on my bed that's a light beige/dark beige small pattern (kinda like small polka dots) and the oil marks are hardly noticeable. Previously, I had a dark purple satiny sheet and the marks were quite obvious.
I've also has luck using some dish soap to help spot treat stubborn oil marks. Dish soap is designed to tackle grease, but don't let it sit too long.