Try Greased Lightening or the Mr. Clean Magic Eraser sponges.

The Greased lightening might also remove some of the paint, so be careful with that. I have the same situation as you; can't afford to tile near the stove, and lots of stains on the walls. My walls are glazed, so that might effect the fact that the Greased Lightening has lightened up the paint, so I would test it out in a small area to be careful.

I once lived in rented apartments, mosy had tiny kitchens. I put mylar Contac paper behind the stoves to catch any grease spatters. I cleaned the mylar with Greased Lightening spray cleaner . I stripped the mylar off each time I moved. Didn't want the landlords blaming me for ruining their walls.

Try TSP (Trisodium phosphate) works great on drywall.

TSP is available at hardware stores