According to
Clean Your House & Everything In It, by Eugenia Chapman & Jill Major, blend the following ingredients to clean your fine wood cabinets: 2 tablespoons of linseed oil, 2 tablespoons of turpentine, and 1 quart of boiling water. Wear rubber gloves, dip a rag in the cleaner, wring it out until it is barely damp, scrub small areas (one door at a time, for example), and wipe it dry immediately. This also is a super blend for cleaning fine furniture, but remember that water should never be allowed to let stand on or soak into wood. When the cleaner cools off, the oil and turpentine will separate from the water. Throw out the cleaner (don't reheat it in your microwave), and make a new batch.
By the way, Lin-sol, a linseed-oil base soap, is best for metal, painted, imitation wood, Formica and plastic kitchen cabinets.
You may think a cleaner that includes water is not proper for use on wood, but chances are, the spray cleaner you currently use is loaded with it. Interestingly, furniture oils are not always the answer either, because oil alone does not work well as a grease remover.
An after cleaning measure: If grease has been a problem at the underside of your cabinets, try using a protective layer of clear contact paper. Next time you plan to entertain, pull it off and voila, no grease!