Cooking oil works well on some surfaces - that is, surfaces which are more or less immune to oil. Wood, metal, plastic. However, wall paint (or wallpaper) are porous and absorb the oil, which remains trapped.
I personally used the cooking oil trick on a wooden door frame, and it worked like a charm. But the wood was protected with lacquer.
Post-factum, I guess that the only way to have a nice wall is to repair the paint. A good specialist might be able to fix only the affected area, but I guess that you get the best result if you clean and repaint the entire wall (you can hire a specialist if you do not want to get messy yourself).
Here’s some common household items that will help remove grease/oil stains from painted walls:
1. White vinegar.
Mix one part white vinegar with one part hot water. Use a spray bottle to apply the solution to the grease. Allow it to set for several minutes and then wipe with a clean rag. Work in small areas and repeat as many times as necessary to get the wall clean. If the area is large, use several rags to collect the grease.
2. Baking soda.
Make a paste of three tablespoons of baking soda with one cup of warm water. Work the paste into the grease stain. Gently rub the area with a nylon scrubber until the stain disappears. Wipe clean with a clean damp rag.
Mix two cups of household ammonia with one gallon of hot water. Use a spray bottle to apply the solution and scrub with a nylon sponge or brush to remove the stains. Gloves and ventilation are a must when using ammonia.
4. TSP (Trisodium Phosphate).
TSP is a strong cleaner. It can cause irritation and even burn if it is used incorrectly. Wear rubber gloves, safety goggles, and long sleeves to protect your skin and eyes. Surfaces outside of the affected area should be protected from TSP splashes as it can discolor or de-gloss paint, wood, and metal. A solution of ¼ cup TSP per gallon of very warm water is a good place to start. For heavy grease build up, increase the ratio to ½ cup TSP per gallon of water. Use a sponge to apply the solution, wringing out the sponge to avoid dripping. Working from the bottom up reduces streaking. Allow the solution to sit on the wall for two minutes to soften the grease before scrubbing with a nylon scrub pad. Rinse the affected area thoroughly as any residue left on the wall could prevent paint from adhering.
Personally I have had the most luck with baking soda and prefer it since it is easy to get and doesn't turn your home into a science experiment. You may also need to paint the wall when done either way but painting before you handle the oil stain will cause it to bleed through the new paint.
Gently scrape off the adhesive while you apply heat on the surface of your wall with hairdryer or heat gun. Then clean with like a baking soda paste & toothbrush. This has worked for me. My kids when younger put stickers on their bedroom wall, me trying to be the fum mom allowed it for a short time.
Other things we've tried in the rentals:
Things to try: WD-40, Goo Gone, acetone, nail polish remove, or rubbing alcohol, then use a rag with a bit of texture to it (example terry cloth)
Laundry detergent or baking soda with a little water to form a paste then with a brush (like a toothbrush for small areas) gently spread the solution over the gummy portion until it is removed, then rinse with clean warm water.
Depends on what type of glue & how long it has been there. Good luck! The heat method worked best in my opinion.