Answer:
Every supermarket sells a cleaning product called "Murphy's Oil Soap". Mix it a bit stronger than recommended on the label, and thoroughly wash your cabinets. One good thing, you don't need to rinse. You may decide after the fact that they need a second washing - if so, do it. Once they are truly clean, and not greasy anymore, use the product called "Cabinet Magic" on them. You're talking about a lot of "elbow grease", but it will work.