Buttercup, my kitty Abby had the same symptoms-runny and "goopy" (not at all firm) poo, extremely stinky and she was definately going outside the litter box because it became evident from the smell that it had happened. I got her into the vet right away and it turned out she was dehydrated, and had a viral infection and some other digestive malady, the name which escapes me. She was about 4.5 months old at the time.

She ended up getting a sub-q treatment to hydrate her as well as an antibiotic and stool hardener, plus she got wormer treatment in order to stop them from developing. After a week or so, she was much better.

Dehydration can weaken kittens quickly and their immune systems aren't as developed so they do not have the reserves of older cats. You can take a look at his gums and if they are not a rosy pink and wet, he is dehydrated. If his gums are tacky to the touch, he is dehydrated. I learned this the hard way as we lost a kitten, Nina, this way so please get Hank to a vet. Please let us know how things turn out. He is such a handsome fellow.