If you want to make your story weird. Screw around with one and only one of these three: Setting, Continuity, or Character
Kafka created surreal stories so compelling because the world they are in are otherwise so normal, so drearily mundane in both setting and characters. If he instead wrote sci-fi books the reader would feel cheated, surrealism builds on breaking the rules reality is based on. If you wrote those rules that you are breaking then you are just cheating.
The same goes with a really strange character, say Dexter Morgan of the show Dexter*. We can get away with portraying a sociopathic, alien mindset so different from any normal character development because he is placed in a very well defined cop drama genre, with real world physics and real world problems**. It is the fact that he thinks about safe driving and buying groceries in between cold blooded murder that makes the character not a caricature.
Contrast these with any of the greatest Sci-fi authors. The heart of science fiction is ordinary people dealing with extraordinary situations. What are people like in a utopia, what will we do when the moon is destroyed to fuel an alien mothership, how will social moors change to accommodate psychic abilities? These and more are answered by the world of science fiction but we only believe them if the reactions come from believable normal people and if the world is (other than the one sci-fi change) normal and believable too.
PS - "There is an exception to every rule, except this one."
There are exceptions to this rule; Robert Anton Wilson's "Illuminati" and arguably Philip K. Dick's "Do Androids Dream of Electric Sheep". If your story must break the rule then do it, but don't think your exceptional just so you can be lazy and not fix up a convoluted or sloppy story.
*Lets just ignore the books here.
**This is half of why we are ignoring the books, especially you Book III -_-


