Well, I don't know about the litter, but I do have a recommendation about the food. When I adopted a couple of my cats, they too came home from the humane society with bags of Science Diet. I too noticed that the food was pretty smelly itself, and therefore their poops were very unpleasant. Science Diet isn't all that great of a food at all I've realized. I've figured out that the only reason why it's considered a great food and is so expensive is because they are selling a vet-recommended/endorsed food, so they can get away with selling a crap-food. Something that is quite a bit cheaper, yet still a very good food (IMO, others will/may say differently) is any of the Nutro foods. I don't feed it, I feed a cheaper, local grain-free food, but if I didn't have access to that one I would feed one of the Nutro Max Cat formulas. It doesn't smell so bad when you open the bag, and their poops are always nice, non-stinky, and firm when they're on it. You will save money if you buy Nutro instead of Science Diet, not only on the food but on vet bills
I've always had good luck with Tidy Cats, so I don't think that that's the problem. It's made mainly to mask odors, more-so than other brands. Within the past 6 months or so I've switched to an unscented, all-natural clumping litter and that seems to work very well. Plus it's like one of the cheapest ways to go when it comes to buying kitty litter. I also use Tidy Cats clay litter (there are 4 boxes, 2 clumping and 2 clay). I think it's the antimicrobial odor control stuff, but I think that all of their clay litters are pretty much the same (except for the crystal type of course). But this combination seems to work very nicely- I only need to change the clay about once a week or so, and I very rarely change the clumping, since it is so good on odor and I keep it so clean in the first place.
(sry I tend to type wayyyy too much, ignore my babbling lol)