Cabinet doors near a stove go tacky long before they look dirty. What is on them is not dust, it is airborne cooking oil that condensed on a cool surface, cooled, and then caught every particle of dust that floated past afterward.
That is why wiping harder does not work. Water and a general-purpose spray push the film around rather than dissolving it, so the surface looks clean while it is wet and goes sticky again as it dries. Grease needs something that breaks it down, plus enough dwell time to work.
The order matters. Start high, at the range hood and the cabinet doors above the stove, because everything you loosen runs downward. Spray a degreaser, wait the full minute or two the label asks for instead of wiping immediately, then work with a clean cloth and rinse the cloth often. A cloth that is already loaded with grease just redistributes it.
Hood filters are the one part almost everyone forgets, and they are the easiest win in the kitchen. Most metal mesh filters lift straight out and can soak in hot water with dish soap while you clean the rest of the room. Ten minutes of soaking does more than ten minutes of scrubbing.
Be careful with finishes. Painted and laminated cabinet doors do not like strong solvents or abrasive pads, and stainless steel shows every wipe that goes against the grain. On stone counters, avoid anything acidic: vinegar and lemon will etch marble and travertine permanently.
As for keeping it away, the honest answer is ventilation. Running the hood while you cook, and for a few minutes afterward, keeps a large share of that oil from ever landing on the cabinets. Everything else is just cleaning it up later.