Well, I haven't really cleaned my cabinets right above the stove for a few years so now they are covered in sticky, nasty goo that's basically settled oil fumes (I like to fry and sautee stuff). Any idea what to use to clean it? I tried regular soapy water through a sprayer but that didn't do much.
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.
Use a NaOH solution. Sodium hydroxide will saponify the fat, which will make it pretty easy to remove it with water (the molecules will have a hydrophilic and a lipophilic part). At the same time, you will disinfect the area you clean. Since NaOH is a strong alkaline, pretty much all bacteria and molds will die very quickly. Technically, KOH (potassium hydroxide) will work even better, but I didn't use that one yet.
It's also very cheap, since it's an extremely common chemical used for a vast number of things.
Be extremely careful when handling sodium hydroxide (caustic soda, NaOH)
Don't let it come in contact with your skin. Being a strong alkaline, it's very aggressive towards organic material. Always wear rubber gloves, easily removable clothing as well as eye protection and air the room as you work with it.
Should it come into contact with your skin anyway: hold the affected skin area under running water for several minutes and consult a doctor.
Put the NaOH into water, under NO circumstances water on dry NaOH! When it dissolves, it releases a lot of heat, so use cold water if you don't want it to start boiling. Also note that NaOH will dissolve aluminium in a rather violent reaction which also releases hydrogen gas. So keep it away from aluminium.
While caustic soda is an excellent cleaning agent, it has to be handled with utmost care. Only use it when all else fails. After you are done cleaning with it, wipe all surfaces that came into contact with NaOH with citric acid or vinegar to neutralize any residues of it.