I had read Metamorphosis by Franz Kafka a long time ago. I have to say, call me stupid, but unless the book was meant to be funny, I didn't actually figure out what being "Kafkaesque" is all about! I happened to read two more short stories by him now, and I might just have gotten closer to solving the mystery.
Das Urteil (The Judgement) I read, very painstakingly, in German. I think I read the dictionary more than I read the book! Anyway. From what (little) I understood, it is a story about the relationship between a father and a son. It is the conflict between the worlds of the father and the son, their lives which Kafka ultimately links with society. The first half of the story is from the boy's point of view, about his life and the people he knows. When the elderly father appears, he begins immediately to criticize and blame the son. By the end of the utterly unreal interaction between the father and the son, the elderly man sentences his son to death. The conflict can only be reconciled by violence and pain, when, in a bland dream-like manner, the son commits suicide. (Or...I can always say I didn't understand much!)
The other story that I read was A Report to An Academy (Ein Bericht für eine Akademie). This one I read in English and actually understood/liked. The story is a report made by an ape to a meeting of a Scientific Academy, an ape who has integrated himself into human society. The ape talks of his former life. The reason the ape first decided to imitate humans was to be able to stay out of a zoo. Now, the ape can hardly remember his animal life - on the other hand you can still make out that his humanness is not natural. He belongs neither here nor there! When the ape finally managed to establish himself in human society completely, he also lost all his freedom. The story can be two things. First, changing oneself according to whatever challenges one faces, adapting to our surroundings - albeit without being fully successful. Second, it is about human nature and freedom (rather, lack of it) in society and existence.
So what do I think Kafkaesque means? Now that will require another post entirely! Let's just say; in his non-romanticized stories of life and struggle; he graphically describes the inner conflicts in all our minds, which is what makes his bizarre and eerie ideas so appealing!