TSP, trisodium phosphate or Krud Kutter.
I always use Murphy's Oil Soap.
If they are really bad, use TSP to get the worst off, then follow with Murphy's Oil Soap and rinse and dry with a soft cloth.
Have you tried a product called Awesome? It can be found in your local Dollar General Store.
Krud Kutter is my recommendation.
Murphy’s oil soap
Hi Kathleen. I'm Cindy. If there is a build up of grease or grime, start with a bucket of warm water. Add a quarter-cup of white vinegar, and a couple squirts of Dawn dish soap. Scrub your cabinets with this solution. After they are dry, go over them again with Murphy's Oil Soap. The soap will clean anything left behind and the oil will condition the wood. Use Murphy's Oil Soap according to the directions on the bottle. Good luck Kathleen and Happy Holidays.