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ORIGINAL: EscalonJon

You could try something like Woollite and carefully clean them without getting them too wet.

Believe it or not, though, seatbelts should be treated with care in order to do what they are supposed to do (save your life) when they are supposed to (in a collision or upset). If a seatbelt is pinched, torn, badly sun damaged, or the stitching is compromised, they should be replaced. If a retractor/tensioner is doing wacky things, I would think about replacement as well.

It may be a good idea to check out replacement belts on the internet and just replace them if they are really, really, soiled. Looking good is one thing, correct functioning is another.