The good news is, the damage isn't really permanent. If it's too difficult to wash in it's current state, cushions can usually be taken apart, washed, and put back together with the slightest of sewing "skills" (ie, the ability to put a needle and thread through a piece of fabric).
I've done this before with pillows that are simply too big for the washing machine.
Go to the dollar store and buy a bunch of large mesh washing bags - the kind that zip up.
If there are stitches to make those little comfortable quilty-type divots, take them out. Use a needle and contrasting thread and mark where those divots were. You'll want to stitch them back in when you're done.
Find a seam. Rip it open about 12-18" or so - narrow enough that you can stitch it back up by hand, but wide enough for you to rip out the stuffing. Take care not to rip the fabric, just open up the seam.
Pull out the stuffing and pack it into the washing bags. Wash the stuffing and the cushion cover. You may need to do this in two loads of wash. You may also need to wash it twice. Run it through the dryer with a bounce sheet or something to make sure the scent is good and gone. (As a side note, I cloth diaper and find that a wash with baking soda, a wash with laundry detergent, and a rinse with cold water is pretty good at removing the stinkiest stinks).
Put the stuffing back in the fabric and stitch your hole back up. Here's a good youtube video on closing up a pillow seam: http://www.youtube.com/watch?v=5CjOXMuTFXo
Fluff pillow so the stuffing is spread out nice and evenly. Get a nice thick, long needle and a heavy, matching thread or thin yarn. Restitch the little divots (sorry, I don't know the technical name for those little puckered in spots) by drawing the needle and thread all the way through both sides of the pillow. Two or three stitches back and forth should hold it. Do that for each spot where you marked a divot.
Your pillow is now totally clean and laundered. The cat hair and stinky pee is all gone. Washed away clean with a nice detergent. Fresh and new. And not $50.