I just throw the whole seat cushion/fabric in the wash - on my chicco keyfit 30, it's really not that difficult to take off and put on. It also took a surprisingly short time to air dry.
I haven't done anything to the straps - but I would read your manual. It's not recommended to use anything terribly strong on the straps, mostly just a damp rag.
Re: cleaning car seat
DS born 6/2013