'One day he'll give up and take a dump on my pillow instead'
One of our cats (the autistic calico one) will use the usual location of the cat tray whether it's there or not. And (if it's not) will still scrape at the carpet, trying in vain to cover over what she's just.. deposited.
We tried putting a plastic cover there permanently so that at least the stuff would stay on the plastic until we could clean it up but her claws are sharp enough to penetrate most flexible plastics and so the liquids just ended up seeping through un-noticed.
 Every so often we take it away to give it a good clean. As in 'boiling water with detergent' cleaning, followed by rinsing with lots of fresh water. And, of course, that seems to be the time that her digestive system really, really has to lighten itself..
 Even using good wood-pellet cat litter, the urine smell builds up over time. And she won't use the tray if it smells of anything other than wood-pellet cat litter and cat waste.
 See above. We tried bleach - she refused to use the tray (and we had to replace it). We tried the various things like nilodour that claim to take away smells - she won't use the tray. The above is the only thing that will both clean the tray and ensure that she uses it afterwards.
 Her siblings went o other people - one of whom came cabk to us to say that they wouldn't use the cat trays. We gave them some of the wood pellet cat litter and the cats started to use the tray properly. So that whole brood may be somewhat autistic. Our *hates* change - even moving her favourite bed slightly will mean she won't use it. And, when she wants to go out, she insists on *me* opening the cat door - if my wife tries, the cat won't go out.
 Another of her oddities - she'll come *in* the cat door, but refuses to go out unless I open it for her.
 She did use it of her own accord one - but that was because she was being chased by an interloper male cat. Who was being chased by our dog..