I was going to just use the answer box, but didn’t have enough characters. Hopefully UfYH will see this, ‘cause I fail at Tumblr.
Here is the answer to your problem, superdarkfuntimes: first, dump all of the current litter in a bag. There is no nice way to do this, I’m afraid; you may want to tie a towel around your face, ‘cause it’s gonna stink. Take heart: this is the last time you’ll have to do this.
Once the litter is empty, scrape out anything sticking in there and clean it; UfYH would probably say “use vinegar!” and so unless I get disagreement from that quarter, I’ll agree (I used to use boiling water when this was a problem, but vinegar is magic). You’re not trying to destink it—if it’s hard plastic, it’s pretty impermeable—you’re just trying to clean out the nasty crap that grows in cat piss.
Next, pick yourself up some cat box liners. These should be readily available at Petco and PetSmart, and I’m pretty sure even Walmart carries them. To go with the liners you will want CLUMPING litter, like Tidy Cat. This will be more expensive than hard clay litter, but trust me—if you hate cat smell, you want to make this investment. Line the cat box once it’s COMPLETELY dry from your cleaning—cat box liners are essentially very shallow garbage bags (you see where this is going?), so you’re basically putting a Hefty in your bin. Pour 3”-4” of litter in the liner.
Now for maintenance: every day, go in there and scoop out the pee. (This will look like rocks, and should not puff up in your face—the magic of clumping litter!) You can leave the poop alone as long as there isn’t a whole bunch of it. Once a week (please note that mine is a single-cat household; your mileage on timing may vary), close that liner right up, take it out to the trash, and replace the liner. Once a month, give the litter box a good wiping down.
Voila! Problem solved.
Any excuse I can get to bust out this gif: