He may have feline herpes, which means he will have it his whole life, but it doesn’t mean that he will have an active case of runny nose, eyes, etc. Once his immune system gets established, the symptoms should subside.
You definitely need to teach him how not to hang out in the litter box. He should do his business, cover it, then get out of it. Maybe it’s the only place where he feels safe, or is exhibiting a behavior that outside cats do which is roll in the dust taking a dust bath. Some cats will roll in the litter because they don’t have dirt to roll in. I’ve never had an inside cat do this myself.
You can take a warm, damp cloth and wipe your kittens eyes and nose, especially if there is a lot of discharge. Also, you can wipe his fur all over too. There are cloths specially made to do this with cats. Or, while he is young, you can even bathe him, making sure to avoid his ears and head with a lot of water. Some cats enjoy water and the clean feeling afterwards. Make sure it is warm, and when you are done, toweling him off and using a blow dryer on low to dry him thoroughly.
Maybe a trip back to the vet would be in order too to make sure that the URI is getting better or there is something else causing his smell.