The name of the fish "Stör" is the same as the word "disturb". That alone offers a lot of potential for bad puns.
It is also weirdly common as a part of other words that don't have anything to do with fish. And third, there are parts of words that sound similar to Stör.
Take all those ingredients and you can have a lot of fun with strange word combinations and only native speakers have a realistic chance of understanding.
It's a type of fish, and they are making word plays with the name of the fish. Why? I'm not sure of the origin of this one. I imagine it's like the beans or the beef stroganoff memes - the origin doesn't matter much at this point.
I actually started with eels. Aal (=> eel) can be inserted basically everywhere by just stretching the "a" a bit, like "Aalle wissen das" instead of "Alle wissen das" (everyone knows that). As far as I know, this started (or at least became popular) via Jan Böhmermann, he had some jokes about that in his show - the same guy who wrote the "goat fucker"-poem about Erdogan that caused massive diplomatic problems and resulted in changed laws.