While Dylan has never soiled outside of his box, he does act like his paws hurt him at times. We took him to the vet and had x-rays done - and two of his paws have sharp bone fragments left behind from a sloppy job. My vet can correct this with surgery but suggested we wait until he shows increased pain or signs of infection. Right now, it is just occasional, as if he gets a pinch now and then All four of his paws were done before we ever adopted him.
So, there are surgical as well as medical ways to help with post-declaw problems. Emily and Eliot show no problems at all, never did and we had their front paws declawed. Lizzie and Robbie are our first with claws - we won't have this done again...and learning to clip the sharpies and take them to a scratching post has been very satisfying because it works!! The clipping was not fun and I did do lots of blood shed BUT, now I can do the kittens and back claws on E&E all by myself and it only takes a few minutes. I seldom bleed at all

For Olivers Meowmie - I really would suggest having his paws x-rayed. It was not nearly as expensive as I thought and then you will KNOW if his paws are hurting him and it cam be corrected.

Another thing you mentioned is stinky and mushy poo. This usually means parasite infections (not worms) but bacterial or amoebic infections and this makes pooping painful. It takes a direct fecal smear to detect (not a flotation). Just ideas!! Hope you find your answers.

Oh and my kitties are VERY finicky about a clean box. They will not use a covered box, prefer scoopable litter and I scoop it at least twice a day. I have four large boxes for five kitties. One of the boxes is a huge rubbermaid "sandy beach" that holds 21 pounds of litter Yup!! FINICKY ABOUT CLEAN.