Sorry to hear of your cat's situation. I did have a cat, Whiskers, that had a similar thing happen to him, except they never knew what caused it and told me it was probably due to degenerative spine (?). I was able to maintain him for 6 months but ended up having to put him to sleep due to the problem he incurred with him having no control of his bowels and urine due to the paralysis (their poop and urine just comes out wherever they are). (see below for that explanation).
But he actually regained some use of his legs for brief periods, like 1 or 2 days and had wonderful success with sterioids (predisone) but he was not put on them until a few weeks later when it was pretty much too late so they were short lived. I am convinced that if he had been put on the predisone right away it may have been better and possibly gotten over it, but I'm not sure sometimes. But here is something that might help you with the OTHER stuff you're experiencing with your kitty: DIAPERS and blue pads.
I'm assuming if your cat's legs are paralized then he/she has no control of his bowels or urine so you must have a real mess (and also dangerous for cat feces to be lying around--very unhealthy for us humans, i.e., parasites).
Here's what I did:
I went online and bought blue pads. They are pads used in hospitals and hospice care for humans, they are white cotton on the top and the bottom is a very thin plastic so if the top gets wet it doesn't seep to the carpet or floor.
However, my cat didn't like to be contained and was very active even if he had to drag his legs behind him, he would, so I created "cat diapers" for him. You can't use doggie diapers or baby diapers because a cat's body is so flexible and the diapers will slide off so i resorted to cutting the blue pads in like a triangle with an opening for his tail, and then securing it with just a smidgen of tape. This was the only thing that worked. But the tape eventually pulls on the cat's fur so you've got to use only a little bit.
This won't cure anything but it will allow you a little more time for your cat. My cat eventually got flys who laid eggs in and around his anus (since his bowels were constantly running) so this is the reason I had to put him to sleep, he didn't seem to mind walking with his legs dragging behind him, but it was the mess from the bowels constantly running (he was 15 years old too).