How can I clean my kitchen wall that has splattered cooking oil on it?

It should come off with a scrub of Dawn dish liquid, baking soda and hot water.

Wash with Dawn dish soap, if won't come off its stained. You'll have to touch up with stain blocker primer like Kilz, then repaint. If your walls are painted in flat paint, they are hard to clean but easy to touch up.

Wash it. Dawn dish soap will work just fine. A vinegar / water solution will work too. Do you have a splatter screen? It does help.

Ban,

Sadly you can't as it will have sunk in. Best bet is to cover it with Stain cover paint and paint with a washable paint or Tile over it or fix a Backsplash or Use Washable wallpaper or Tiled finished Hardboard...........

is it painted? It needs wiped with degreaser Dawn,Krud Kutter then needs primer-Kilz/Zinsser- then painted with semi gloss,gloss washable paint