I think you need to look for a low-dust or "dust free" litter; these are available in both regular and clumping.
If the smell is truly rank, you may need to go on a poo watch! A cat could have developed worms and that's an easy 1-2 pill fix.
Cats, as they get older usually, but sometimes with younger ones, don't drink enough, so you have to supplement their liquid with canned food. As a cat might not be drinking, the urine is very concentrated when it's released and that will have a very strong odor.
If you are using dry food, you may need to switch brands. The easiest way to switch to make a mixture of 75% current food with 25% new food and feed that to them for a few days. Then go to a 50-50 mixture, then 25% original food with 75% new food, and then finally to all new. Sometimes just getting it to a 50-50 is the best you can do b/c cats are finicky and will stop eating if they don't like it or know it. I've known a few cat owners that mixed equal parts of the cat's preferred but poorer quality food with a better quality food and had decent results. I made it a point (and still do) to switch up on my cats; it's all Iams brand but it's different flavors and stuff. I did this when they were babies so they got used to it and will pretty much eat anything we give them... or anything they find like the tassles on my DD's bike, but that's another story altogether!
Unfortunately you're going to have to do a lot of experimenting to figure out the true problem. I would start with the cheapest option (probably the cat litter) and see how that works. The next would probably be changing the food and the vets office would be last unless you think there is something seriously wrong; in that case, a vet appt is always cheapest when you catch a problem early on!