My guess is probably that there is absolutely nothing wrong with your cat (which is good news).....more than likely, you've gotten a bad batch of clumping litter. This happens more than you'd think. I would simply start out by purchasing another box of litter and see what happens. I would even consider a different brand just to make certain that it's not the cat.
Please let me know if I can help further!
You might have him check to see if there is an infection going on. The strong ammonia smell indicates a strong concentration of urine - or high acidity which is what you want with cats. Males tend to have stronger urine than females (especially unneutered males), but if this is a recent development, it definitely should be checked. If he is not drinking a lot, you might try to entice him to drink more - sometimes cat fountains help or putting icecubes in his water bowl. Given his age, I think it would be a good idea for your vet to do a urinalysis and maybe a geriatic blood panel just to see if everything is normal.
Please let me know what they find.