Jokes or irony in the Bible, Koran, Torah, etc...?
Sure. Humor can be pretty dependent on cultural context, so ancient jokes don't always translate very well; but I can think of at least two examples of jokes that still more or less make sense.
When Elijah is taunting the priests of Baal for failing to call down their god's power, he basically says, "well, maybe Baal is on vacation, or maybe he's taking a dump" (1 Kings 18:25-27).
From the Sermon on the Mount: Jesus' counsel to "take the beam out of your own eye" (Matthew 7:3) has become proverbial, but it was intended to conjure a funny mental image.
Besides the funny imagery /u/yeshavesum references, the bible also has a number of puns. These don't usually work in translation, but there's evident wordplay in the text.
One example is in Judges 10, where a man named Ya'ir has thirty sons who ride thirty donkeys ('ayarim) who found thirty cities ('ayarim). The nJPS translation has them riding burros and founding boroughs to preserve the wordplay. Another example is in the story of Joseph in Egypt. When he's interpreting dreams, he uses the phrase "lift up your head" alternately talking about lifting someone's status form ignominy and lifting someone's head from the body by decapitation.
There is a lot of wordplay that doesn't seem to be humorous, particularly with names, where people either are given names that fit them well (which isn't really wordplay at all, just people naming relevantly) or people fulfilling their name through the narrative (such as Ruth, whose name means "companionship").
During the formation of the early church, a group of hyper-religious folk taught that keeping the Law (including circumcision) would make one right with God. In frustration, the apostle Paul said they should just go all in with it and emasculate themselves. (Galatians 5:12)
A couple that come to mind
"And he said to them: 'You have a fine way of setting aside the commands of God in order to observe your own traditions!'" (Mark 7:9 NIV)."
(don't worry about doing what God said, doing things the way you've always done them is MUCH more important)
I've always read luke 11:43-47 as being a sarcastic "Oh you think your better than everyone else" reply to someone trying to shame Jesus
Woe unto you Pharisees! for ye love the chief seats in the synagogues, and the salutations in the marketplaces. Woe unto you! for ye are as the tombs which appear not, and the men that walk over them know it not. And one of the lawyers answering saith unto him, Teacher, in saying this thou reproachest us also. And he said, Woe unto you lawyers also! for ye load men with burdens grievous to be borne, and ye yourselves touch not the burdens with one of your fingers. (Luke 11:43-46, ASV)
Then the LORD said to Cain, "Where is your brother Abel?" "I don't know," he replied. "Am I my brother's keeper?" Genesis 4:9
(what am i, his babysitter?)
Gideon, who calls himself "the weakest in [his tribe of] Manasseh, and the least in my family" was cowering in a winepress threshing wheat because of fear of the Midianites.
The angel of the Lord appears to him and says "The Lord is with you, mighty warrior.”
Judges 6:11-15
Proverbs is good for a laugh. Try Proverbs 27:14 "If anyone loudly blesses their neighbor early in the morning, it will be taken as a curse." Next time yourneighbor wakes you up and 27:15 "A quarrelsome wife is like the dripping of a leaky roof in a rainstorm;".
Jesus yelled at a tree because he was hungry once, that is pretty funny.
Mark 11:12-13: "12 The next day as they were leaving Bethany, Jesus was hungry. 13 Seeing in the distance a fig tree in leaf, he went to find out if it had any fruit. When he reached it, he found nothing but leaves, because it was not the season for figs. 14 Then he said to the tree, “May no one ever eat fruit from you again.” And his disciples heard him say it."
A lot of biblical work here, anything from the Koran?
Short answer: yes, loads.
Before proceeding, it would be helpful to describe what I mean by “humor.”21 In ancient literature, humor consisted of non-tendentious forms such as wordplays, jesting, and pleasurable charm. Typically, pleasurable charm was amenable to the rhetoric of the elegant style. Humor in ancient literature also consisted of tendentious forms such as derogatory epithets, barbed wit, raillery, derisive hyperbole, fear-evoking taunts, and shock-producing dicta. These types of humor were more commonly associated with the forceful style rhetoric.22 Depending on the kind of humor, responses included smiles, smirks, sneering, derisive laughter, shock, and surprise
So as has been mentioned elsewhere, 'humor' doesn't mean the same thing now as it did then. In a public forum, you make other people laugh at the person you're arguing with as a rhetorical way of garnering support for your side.
That quote is from "Status Disputes and Disparate Dicta, Humor Rhetoric in Luke 16:14-18" - Teresa Bednarz.
That particular paper is a detailed analysis of one particular passage, but a lot of work has been done on this type of rhetoric in the gospels since it's so often used.
There's a bit of sarcasm in the Christian Bible when God rebukes Job in Job 38:18-21
What is the way to the abode of light? And where does darkness reside? Can you take them to their places? Do you know the paths to their dwellings? Surely you know, for you were already born! You have lived so many years!
Here's a list, compiled by a monk, containing examples of humor in the Buddhist suttas:
https://sujato.wordpress.com/2011/11/29/the-ten-funniest-scenes-from-the-pali-canon/
One of my favorite examples of the Buddha's sense of humor is found in the Kevatta Sutta. The Buddha tells the story of a monk who decided to turn to the Gods seeking an answer to a question on the dharma, on the nature of cessation. The monk sets his mind on the heavenly realms and encounters various deities, each of them unable to provide an answer but assuring the monk that a deity more powerful than them possessed it. He's finally led to the presence of the God believed to be the omnipotent and omniscient Creator, the Supreme Lord, and his heavenly retinue. The monk poses his question to this highest of Gods but instead of having it answered, he is met with boasts about God's supposed powers and qualities. He persists with his question, and God evades again and again. Finally, God pulls the monk aside and quietly confesses that he doesn't know the answer but that he didn't want to embarrass himself before his retinue by admitting his ignorance to them. He requests the monk to leave and take his question, as it concerned the dharma, to the Buddha.
In Islam, the main sources ia the Quran and hadith, the latter being records of the Prophet Muhammad's sayings and actions.
I don't think there's any in the Quran, but there's plenty in the hadith. Like:
-Anas said: A man came to the Prophet  and said: O Apostle of Allah! give me a mount. The Prophet  said: We shall give you a she-camel's child to ride on. He said: What shall I do with a she-camel's child? The Prophet  replied: Do any others than she-camels give birth to camels?" [Sunan Abu Dawood; Vol. 3, # 4980; also #4981; #4982]
-One time, there was a large caravan that was coming from outside of Madinah and they had some fruit, some delicate expensive exotic fruit. And Nu’ayman رضي الله تعالى عنه he took it and he took it to the Prophet صلى الله عليه وسلم and he said this is a gift to you. And he told the guys that he took the fruit from, ‘look I’ll pay you guys later. This is a debt and inshAllah I’ll pay you later.’ So he took the gift to the Prophet صلى الله عليه وسلم and the Prophet صلى الله عليه وسلم ate it and the Prophet صلى الله عليه وسلم enjoyed it and then whenever they came to Nu’ayman demanding repayment, Nu’ayman said, ‘I didn’t eat it. The Messenger of Allah ate it. You should go to him and request it from him.’ So these guys go to the house of the Prophet صلى الله عليه وسلم and they say, ‘We want the money for the fruits.’ And the Prophet صلى الله عليه وسلم says, ‘What are you talking about? That was given to me as a gift!’ They said, ‘We want the money for the fruits.’ So Rasool Allah صلى الله عليه وسلم called Nu’ayman and said, ‘Nu’ayman, didn’t you say that this was a gift from you?’ And he said, ‘O’ Rasool Allah I wanted you to eat it and I wanted you to be the first to try this fruit because I felt like you were the most deserving but I didn’t have the money. So O’ Rasool Allah , pay the man.’ And Rasool Allah صلى الله عليه وسلم he laughed صلى الله عليه وسلم and he paid the men.
In Paul's letter to the Galatians, he has this part where he's talking about some early Christians who were insisting that new believers had to be circumcised in order to be saved (he disagreed):
10I am confident in the Lord that you will take no other view. The one who is throwing you into confusion, whoever that may be, will have to pay the penalty. 11Brothers and sisters, if I am still preaching circumcision, why am I still being persecuted? In that case the offense of the cross has been abolished. 12As for those agitators, I wish they would go the whole way and emasculate themselves!
One example in the Islamic Hadeeth is of the Prophet Muhammad (pbuh) joking around with Julaybeeb.
Basically they're in the market and he sneaks up behind him and covers his eyes, Julaybeeb says "who's this?" And the prophet yells to the market, "who would like to buy this prime physical specimen as a servant! He is in great demand, act quickly or you will lose this deal!"
Julaybeeb replies, "surely no one would want me, look at how ugly, skinny, and short I am"
And the prophet replies, "Perhaps, but in the eyes of your Lord you are greater than those 2 mountains combined" (pointing at mountains in the horizon)
Julaybeeb smiles and they laugh together.
Julaybeeb didn't know who his parents were (Julaybeeb is just a nickname meaning "small-grown", he didn't even have a name) so he had no family and no tribe, which made him an outcast in the Arab world at the time. Add to that his appearance and stature and he was basically on the lowest rung of the social ladder (until the prophet arranged for him to be married to woman in a prosperous family, which is an interesting story on its own, I'll copy/paste it below). There are more Hadeeths about him and it is a very interesting story to learn about the culture of the Arabs at that time.
P.S. I wrote this down form memory so if the dialogue isn't exactly the same please forgive me; the story is still accurate enough to retain its meaning.
Marriage Story
With Julaybib in mind, the Prophet went to one of the Ansar and said: “I want to have your daughter married.” “How wonderful and blessed, O Messenger of Allah and what a delight to the eye (this would be),” replied the Ansari man with obvious joy and happiness. “I do not want her for myself,” added the Prophet. “Then for whom, O Messenger of Allah?” asked the man, obviously somewhat let down. “For Julaybib,” said the Prophet. The Ansari must have been too shocked to give his own reaction and he merely said: “I will consult with her mother.” And off he went to his wife. “The Messenger of Allah, may Allah bless him and grant him peace, wants to have your daughter married,” he said to her. She too was thrilled. “What a wonderful idea and what a delight to the eye (this would be),” she said. “He does not want to marry her himself but he wants to marry her to Julaybib,” he added. She was flabbergasted.
“To Julaybib! No, never to Julaybib! No, by Allah, we shall not marry (her) to him,” she protested. As the Ansari was about to return to the Prophet to inform him of what his wife had said, the daughter who had head her mother’s protestations, asked: “Who has asked you to marry me?” Her mother told her of the Prophet’s request for her hand in marriage to Julaybib. When she heard that the request had come from the Prophet and that her mother was absolutely opposed to the idea, she was greatly perturbed and said: “Do you refuse the request of the Messenger of Allah? Send me to him for he shall certainly not bring ruin to me.”
I found it funny when Solomon's son, Rehoboam, takes over after Solomon's death, he seeks out advice on how to handle his subjects' request to lighten the hard service that Solomon had put on them. He gets the advice of the old men which is to be kinder and gentler. Then he goes to the young men for their advice. They advise contrary to the old men and tell him to tell his subjects that his little finger is thicker than his fathers thigh and he will add more work to their burden. But, by little finger, he meant his cock.
There's a litote in the Book of Mormon I always found funny:
Helaman 4:13 And because of this their great wickedness, and their boastings in their own strength, they were left in their own strength...
In Snorri's edda, Thiarce's (a giant wizard guy) daughter, Skadi, threatened to kill the Aesir (the Norse gods) if she isn't given a husband and made to laugh to assuage her grief.
Loki ties his testicles to a goats beard and plays tug of war with it. Needless to say, she laughed.
Later on in the stories, Odin and crew are going up a previously journeyable river. It's rough and it threatens to kill them all. They manage to get quite a ways up the river and find a giants daughter (popular trope I guess), with (I'm paraphrasing for clarity): her legs akimbo over the river and the source of the rough water coming from her. Ie. She's peeing into the river which is causing it to overflow. One of the gods hurls a large boulder at her which "strikes it's mark." Ie. He threw a rock and hit her in the genitals.
It's very slapstick. And is a currently used religious text (sort of, text is too strong a word).
Source: these stories appear throughout the prose and poetic edda and some other collections as well. They are repeated, I'll give a specific source when I get home from work.
All of the responses here seem to be Biblical. Anything from the Koran, Mahabharata or others?