How to clean settled oil fumes from cabinets?
If it's safe for the cabinet surfaces, Bar Keepers Friend or some similar product (the active ingredient is oxalic acid) is pretty good at dealing with gummy polymerized oil mess. I would not try this on finished wood or painted surfaces, but if you happen to have a metal vent hood above the stove it's fine, or if you're dealing with the hidden unfinished underside of the cabinets.

Failing that, the stronger the soap the better. Soapy water may not do much, but if you squirt a good amount of dish soap into a moist sponge, you may start making progress.

See also Gummy residue from baking spray/oil - this is essentially the same thing as those dark spots you get from stray oil when baking, but generally in larger quantities and possibly a more liquid or at least softer form.