The problem with the grey cloth seats is that there really is no waterproof backing to the cloth. Sure the foam pads get a very light wrap in plastic from the factory, but thats meant to aid in the assembly not to provide protection for the foam.
If you want them TRUELY clean I recommend removing them from the seat frames and actually just washing them in a good washing machine (I like the big ones at laundromats). Dry them on medium/low heat so as not to shrink them then reinstall on the seats. They really arent that hard to take off the seats and that will give you the best results. Thats a good time to lube up your seat tracks and motors as well, and since you want to do the carpets too, and I recommend removal for cleaning, you have to take the seats out anyway.
For carpets, you need to pull the front seats, the console and the front legs of the back seats, as well as the kick plates in the door sills. Then the carpet comes out very easy for cleaning. Then carefully peel off the jute padding trying not to stretch it or shred it too much, and set it aside to put back later.
At that point really any carept cleaning solution you want to use will work. As I mentioned earlier I just use a little dawn dishsoap, some Purple Power degreaser and a dash of bleach in a 1Gal garden sprayer filled with hot tap water. Soak, scrub, rinse with lots of water from a hose or pressure washer (I use a pressure washer and its not too harsh on the carpet), repeat as needed.
Then hang the carpet to let it dry. I just use a 6ft step ladder with a 2x4 on top to drape the carpet over. After a couple hours of hanging dry I hit it with my wet/dry shop vac to get most of the remaining water out of it and suck out any remaining dirt particles. I move it over near my woodstove after that but if you have a couple nice dry days, just air drying works.
Using 3M super77 (or similiar) stick your jute back where it belongs and reinstall everything.
A trick to help getting your seat covers back on is to use movers wrap (saran wrap on a much larger scale) to loosely wrap the foam first. This lets the fabric slide over easily and provides you a slight amount of waterproofing after all is said and done.