At our house we try and stay away from microwave cooking wherever possible, which consequently means that we use the stove that much more than average. We have a fan hood, but over the years cooking grease has still built up on the kitchen ceiling and it's starting to look, frankly, a little gross.
We've tried dawn dish soap and a scrub brush. It worked a little, but after a half a day of scrubbing overhead (and arms that feel like they're about to fall off) it still looks pretty awful.
I'd like to do this more naturally without resorting to harsh chemicals like TSP, but I don't know what else to try.
If you don't "know enough"... try anyway! (Cuz that's how you learn.)
Do you use splatter screens over the frying pans and pots while you cook? A big, flat circle with a handle and a screen across it, sits on the frying pan, the grease mostly clings to it. Then it gets cleaned with a grease cutter. They are in the kitchen sections of stores, even the grocery store used to sell them. If you wanted to make your own, you could make a frame with wire, include a handle, and cover it with 100% cotton fabric. It collects so much grease you wouldn't want to put it in the washing machine but maybe hand-wash it in a bucket with soap.
You can use a floor sponge mop to reach the ceiling sprayed with a grease cutter like 409 or whatever kind of environmentally friendly grease cutter is available. Of course, floating grease isn't just on the ceiling. It's on the walls, it may have floated into rooms with fabric on chairs and couches, and lamp shades. If you are noticing a greasy surface on a side table in another room, then it's on everything in that room.
It's probably not a good idea to be breathing floating grease, and maybe cooking at a lower temperature to keep that from happening. Haven't there been articles lately about how oil taken to temps over 400F or 450F turn into something that isn't good for us?
If you are an avid fryer of foods there are very good air fryers on the market that everyone raves about. Check out YouTube for people doing different recipes in an air fryer.
Don't fall for the My-Place-Is-Special, It-Won't-Happen-Here Syndrome.
Chemistry 101 tells us: like dissolves like. That means for an oil based problem, you need an oil based cleaner. I'm still finding organic replacements for what I used in the past (i.e. Murphy's Oil Soap), but that's where I would begin.
The only real way to shift that is a steam cleaner, and depending on what your ceiling is covered in it may take that off to. Our last house didn't have a cooker hood/extractor so I used to wash the ceilings and beams every 2-3 months, if you do it often nothing more than brown soap and water is needed.
Best thing for grease is undiluted dishsoap. Put on your hands and coat evenly and let sit a while. Damp sponge after that. If its really bad you can use TSP (tri-sodium phosphate) but you want to keep that off your skin.