Paint is usually hard to clean unless you have special paints. Some things you can try are:
Using sponges not cloths. This promotes dabbing not rubbing which removes paint.
Use mild soaps or even no soap. Yes, dish soap is good for grease removal, but it is not good for paint. So use mild soaps and try to extract the oil from the paint. Using flour or cornstarch on the wall helps drag the oil out and then dabbing clean with a wet sponge works. Not using soap at all helps keep paint intact.
Lessen exposure to moisture on the paint to as short as possible and try not to rub or dab paint very much. Also, try not to wait to treat stains clean them immediately.