We use Murphy's Oil Soap, and it works well.
I use TSP to clean mine.
Dawn dish detergent in warm water in a bucket or dishpan, magic erasers, a toothbrush with soft bristles, and microfiber cloths.
This is how I do it---- I remove any grease by wiping the cabinets with a soft cloth that has small amounts of oil on it. Oily products break down greasy, oily messes. Followed by sprays of Windex, also applied with a soft cloth (old t-shirts work great!)