Thanks to the vast myriad of Cutaway Gags and the overall wackiness of the main cast, the world of Family Guy oozes weirdness from its core. There's a one year old baby who built a functional time machine that led to the creation of the universe, a talking dog that has long term relationships with human women without anyone commenting, a woman who was pregnant for "like 6 years" (as Peter put it), numerous anthropomorphic talking animals and inanimate objects (with the evil monkey who lives in Chris' closet and the giant unkillable chicken being two of the most frequently-appearing ones), a peg-legged pirate whose father may or may not have been a tree, and the Kool-Aid Man who bursts into people's houses while yelling "OH YEAAHHH". This is just the tip of the iceberg. There's also:
- God having an arm-wrestling match with his roommate Chuggs, then creating the Big Bang by lighting a fart.
- The time Peter (and later, Quagmire) was somebody's glass eye.
- Ben Stiller flying with his ears.
- MC Escher's rap video where he defies the laws of physics by "going up the sideway stairs".
- A bunch of wheelchair-bound people forming a Humongous Mecha.
- Peter's Mexican farts taking corporeal form and shooting up the house.
- A mentally-handicapped rooster screaming "GOOD NIGHT EVERYBODY!" at the crack of dawn.
- Stewie being used as a football.
- Goofy going to Hell for being somehow involved in 9/11.
- A high-powered toilet sucking all of Peter's clothes off the second he flushes it.
- The Pink Panther showing up and telling Brian "Welcome to Hell" after he gets spray-painted pink.
- A story about a wolf being tricked into saying "Cock-a-doodle-doo" that ends with him turning to prostitution.
- Mayor West chasing the pizza delivery guy off with a cat launcher.
- Timer The Cheese Guy keeping people up at night because he "smoked a whole bunch of crack".
- Peter being cast as the straight line block in Tetris (and screwing it up because he moved at the last second).
- A Palestinian alarm clock that blows up like a pile of C4 when it goes off.
- An experimental drug that turns the user into a squirrel.
- Peter and his friends getting drunk and driving a car down a water slide (how it even fit, we'll never know).
- Peter's head exploding after he ate half a popsicle in one bite.
- A slinky looking up anal sex porn.
- Mayor West's indestructible moustache (indestructible as in "using a chainsaw to try and cut it off destroys the chainsaw).
- Stewie's tricycle being fitted with a car bomb by a disgruntled Instagram fan.
- Peter taking drugs causing him to turn into a live-action version of himself.
- Peter trying to fix a blocked toilet with a baseball pitching machine and flooding the entire house.
- Chris' pet goldfish (which he flushed down the toilet because he thought it was dead) having mutated in the sewer and holding him at gunpoint.
- The Griffin men acting more cultured, only for Peter to spontaneously combust out of nowhere and treat it like a minor inconvinience.
- Child Protective Services taking away Peter's houseplant because he accidentally overwatered it and gave it too much sunlight.
- Quagmire impregnating a giraffe, then denying the resulting offspring is his.
- Peter's pet tropical fish having to pay for his doctor's bill.
- A doctor using a defibrillator on a patient causes them to explode into Ludicrous Gibs because the doctor forgot to say "Clear!" beforehand.
- An inflatable tube-man getting into a shootout with the police.
- A tour of the fire station ending with a controlled flame committing Murder-Suicide.
- Peter turning his house into a giant puppet (and later a hot air balloon).
- The last M&M in the Griffins' advent calendar plotting to kill them all for "eating his entire family".
- Peter drawing a spaceship and flying off in it to get out of a haircut.
- Quagmire getting trapped in a bubble and floating off.
- A couple arriving in New York and being carried off by a pterodactyl mere seconds after they step off the plane.
- Lois being stalked by the narrator from Caillou.
- Target having a security system that lasers runaway employees to death.
- Peter using Brian as a replacement moustache.
- A high-school teenager using Peppa Pig to fake her own death.
- Hitler juggling fish while on a unicycle.
- Adam West sending the host of Jeopardy back to the 5th dimension "where he belongs" by getting him to say his name backwards.
- Steve Buscemi's teeth coming to life, arguing with each other, and popping out of his mouth.
- The ER having a ward specifically for pancakes.
- Chris' head exploding upon finding Peter's porn collection.
- A plate of fish and chips singing about how fat guys think they're a healthy food.
- Peter turning the outside of his house into a makeshift Donkey Kong level.
- A Bar Fight between a stick of broccoli and a Brussel sprout.
- The White Cliffs of Dover talking to each other about travel insurance.
- Peter using two metal detectors in close proximity causing him to break reality.
- Peter going on a date with a stick figure.
- One episode of Two and a Half Men being filmed in front of a live ostrich.
- A man consummating a relationship with the tree stump outside his house after his wife lectures him about it and gets blown up.
- Fozzie Bear's ill-fated stand-up gig in Saudi Arabia.
- A hawk practicing BDSM with Cleveland's drone.
- Blue and Yellow splitting up for an unexplored reason.
- Peter taking a job as Matt Damon's neck.
- A gay guy from church camp pursuing a relationship with a talking moose head.
- Cleveland being put in a Plinko machine.
- A (literal) Stubborn Mule arguing with a guy about whether or not Kevin Bacon was in Footloose.
- Joe's phone ringing when he's in the middle of a rant, causing him to yell at the phone to shut up, and the phone responding in a "Sheesh, okay!" tone.
- Peter making the "Is your refrigerator running?" crank call to an actual refrigerator, who then comes round Peter's house and beats him up.
- The easily-startled wallpaper that screams and rolls up when anyone comes into the room.
- The nature documentary in which "a flock of Jews" fly away after witnessing a Black woman and an Italian man get into a confrontation.
- The Pewterscmidts' maid having a son so morbidly obese that he rolls everywhere.
- A Japanese weather balloon getting angry at Peter (who's equipped with a makeshift jetpack) for mistaking her for a Chinese one.
- Chris and Stewie's attempt at running a lemonade stand ending with the lemonade tricking Chris into the jug and running away, while claiming that "lemons are God's children".
- Lois pouring Peter's Red Bull out in the yard causing a flower to gain sentience, uproot itself, hijack some poor bastard's car on "official flower business", and drive off.
- Lois repressing her feelings about Peter's negative behavior causing her to develop a (singing) tumor with Peter's face on it.
- Peter and Brian trying out a sensory deprivation chamber and coming back out moments later with their heads switched.
- Peter making a morally dubious decision because his shoulder angel got stuck in traffic.
- A giant crab preventing guests from entering Peter's house.
- Mexican Peter jumping into a Flying Saucer shaped like a giant sombrero and flying off.
- A cow ordering steak and cheesecake from a steakhouse.
- Quagmire hiding inside a turtle.
- Peter's pet rock pissing on the carpet.
- A giraffe attending a baseball game and pissing off the people who got stuck behind it and couldn't see the game.
- Peter feeding his mogwai after midnight causing it to turn into Fran Drescher.
