When oil splashes onto your kitchen walls, you may be left with a stubborn stain. I had the same problem with the faux plaster finish in my kitchen. While frying potatoes, I splattered some oil onto the walls and it left stains. To remove them, mix a mild dishwashing detergent, like Dawn, with warm water and apply it to the stains with a sponge or rag as shown. The detergent contains a grease cutter that should remove the stains.
If the stain has been on the wall for several months or longer and won't come off with detergent, brush a primer over the stains. Then apply a fresh coat of plaster over the primer, wait for it to dry, and add the topcoat.
In the future, if oil splashes on the walls, use this fix immediately. The sooner you clean, the better the results.