What's the best non-caustic way to clean my 25 year old garage floor?

try white vinegar and water add some blue dawn

I would start with straight Mean Green cleaner in concentrated form, with a large scrub brush. Then rinse with a power washer.

I'm with Missy.....start with a good concentrated cleaner & warm water and some old fashion elbow work and knee pads. OR some vinegar & water. If all else fails, try TSP and hot water. It's tri sodium phosphate. You can get this in a non phosphate formula, but wear gloves and a face mask if you've never used this product before. I've used it for many projects with no adverse reactions, but great results. Be safe and best of luck.

Warm water and laundry detergent mixed in a bucket of water and follow that by a good pressure washing.

I'm s sure there are liquid cement cleaners, you can buy, at a Home Depot or Lowe's to clean the garage floor. After your done roll on some cement paint to finish the job. They have many colors, and styles. You can make your floor say dark blue with speckles. When you work with this it's somewhat toxic, but it looks very nice and the smell goes away. You roll this on, you'll need, gloves, mask, and protective eye wear.