If they are not finished wood - use sudsy ammonia.
Murphy's oil soap
Try using dish washer power! Super helped me :)
what is dish washer power?
Murphy's oil soap, or mix in a spray bottle a half cup of white vinegar, a half cup of dawn dishwashing liquid, and two cups of warm water, and use it.
I just cleaned my oven with baking soda and vinegar. Try this on a small part of your cabinet. it may just work
Dawn dish soap. Magic eraser is my go too also. Good luck.
Thank you for asking this question. The answers you got are so helpful!
Probably a spray on or brush on Degreaser, maybe Eucalyptus Oil.