(When someone seems to have something wrong with them, but it's nothing, we call that "kutyabaja" in Hungarian ("dog's problem"). So the joke is: "- Is Petey okay? - Sure, look! He only has dog's problem!" (the joke being that Petey is full of fleas, which is a real dog's problem.)
Octopollyparrot ("Polly" is a standard name for parrots, and "polip" is "octopus" in Hungarian)
Trojan diner / befaló ("Fa" is "wood", ló" is "horse" in Hungarian. Next to each other they form "faló", which can also mean" eatery" or "diner" So "Trojan diner" also sounds like "Trojan wooden horse").
This joke plays on the word "halálom", which means "my death". "Halálom" is by chance made up of the words "hal" - "fish" and "álom" which is "dream". So "Fishdream" is the same as "My death". The joke is: "Which animal is it scary to dream of? A fish. Why? It's about my death / fishdream."
How does a retired man walk around? - By fumbling around. ("fumbling" is "botorkál" in Hungarian, which starts with "bot", meaning "stick". So "sétabotorkál" is a combination of "walking stick" and "fumbling around").
Otolaryngologist (An ear and throat specialist is "gégészet" in Hungarian, while the sound geese make is "gá gá" in Hungarian, so "gégészet" becomes "gágászat")
"Hajbókolás" means giving compliments to someone (like royalty), but in this form "haj" also means "hair", and "bókolás" means "paying compliments to someone". So the man is complimenting the hair.
A new verse for an old children's song. The original: "Knifes, forks, scissors are not to be held by children." The new verse: "Nets, bags, and sacks are not to be put on children's heads."
- Want a pizza? - Absolutely (feltétlenül). - What toppings? - I said absolutely. ("feltétlenül" is not just "absolutely", it can also mean "without topping")
Happy harvest/birthday! ("Születés" is "birth" in Hungarian, while the very similar "szüretés" is "harvest".)
- Fear me, evil doers! For it is I, Blood Man! - Ugh. That is a terrible name, Master Bruce. - Oh. So what should I be called? - I do not know. Anything, but not blood man. ("but not blood man" translates literally to "de ne vér ember", and "denevér" is Hungarian for "Bat", while "ember" is "Man". 🙂
- Good day to you! I cannot cross this river. Could you make me a bridge, elder master? - Weeell... I've grown rather old, my back is killing me and my knees hurt... Still, the old man made a bridge. (The joke being that "making a bridge" also refers to a gymnastic exercise where you bend over backwards.)
Another name for the arm wrestling champion? - A conductor. (The joke is that Conductor is called "karmester" in Hungarian. "kar" also means "arm" and "mester" is "master").
- And which tree is your favorite, children? - Our chocolate tree ("Our tree" is "Fánk" in Hungarian, which is the same word for doughnut)
Why is the runner-up fencing champion sad? - Because she was an arm's length from victory. (In Hungarian, "arm" is "kar", while "sword" is "kard". So she was "a sword length from victory".)
What do you call the wife of a silkworm? - Silkwife (this is not funny at all in English, however, in Hungarian "silk" is "selyem", which sounds close to "nejem", meaning "my wife". So literally the punchline is "My wife worm.")