If the removeable mats, take them to the self sever car wash, and just spray them down. I did that on just the rinse cycle, and it took out crusted on salt. For everything else, you can use a foaming type of cleaner and a brush. Go to any auto parts store, or better yet, target or walmart, in the auto care department you'll find a bunch of cleaners that are all about the same.
Why don't you go to a self serve carwash that has the high pressure wands to spray the car and accessories with? Choose HOT water with soap to spray the mats and clean them. Then you'll need to let them dry in the hot sun. Use their vacuum cleaner to suck all the excess water and debris from the car mats. You could bring a can of spray carpet cleaner to apply an hour before you arrive at the car wash.