Its just fabric. Use unscented tide liquid (the enzymes help, and it wont smell forever). Dilute about 1 teaspoon in 24 ounces of water, and put in a spray bottle. Spritz it on, scrub with just about any plastic or natural fiber brush that is moderately stiff, suck it back away with a wet dry vac. Repeat as needed on any spot. Follow up doing the same procedure with normal water while its still damp, until no more suds are released from fabric. If your dealing with a stain that seems more oily, switch out for a solution of Dawn handwashing dish detergent. For anything even worse, try a bit of Oxy clean powder.
I did this on the ENTIRE interior of a car I bought, which was full of cigar smoke, ashes, spilled drinks, oil stains, and melted candy. Amazing results.
If the covers come off, all the better, let your washing machine do the hard work of washing it. You may need to prework some spots with the dilute detergent and brush though.
Many parts of that car are microfiber, and that stuff came really clean doing this. The armrests were black with skin residues, and came back to their original color and texture.
Follow up with a knapping brush (lots of very short, metal wire bristles) to correct any texture issues of the microfiber. I've seen something similar sold for removing shedding fur from pets.