After wrecking Popeye's ship and stealing away Olive Oyl, hero of Arabic legend Sindbad decides to test him and his ever-resilient new rival's strength in order to prove their supremacy as the "most remarkable, extraordinary fella" of Sindbad's menagerie island.
Popeye, Olive Oyl and more King Features Syndicate comic strip characters are invited on a cruise hosted by Professor Grimsby, a mad scientist who wants to eliminate laughter from the world. When the ship is held hostage on his island lair, it's up to the much more action-inclined Mandrake the Magician, Steve Canyon, and Flash Gordon (among others) to save the funnymakers from their eternal inprisonment.
Popeye the Sailor, accompanied by Olive Oyl and Wimpy, is dispatched to stop the dreaded bandit Abu Hassan and his force of forty thieves.
Popeye sails to Goon Island in search of his Pappy. He finds the place populated by the imposing, but ugly, goons, and a "no humans" sign. His imprisoned pappy at first ignores him, but when Popeye is caught by the goons and carried off, his can of spinach lands near Pappy and it works just as well on him as it does on Popeye.
Popeye and Olive, adrift on a raft, land on what apparently is Africa, and are immediately battling elephants and gorillas (also a moose!). Popeye eventually battles an entire menagerie at once - after first gulping down a can of spinach, of course.
Popeye skates over to Olive's house to give her a Christmas present: ice skates of her own. While he's teaching her, Bluto skates up and gets fresh; of course, Popeye fights him. When Olive rejects Bluto again, he sends her careening on an ice floe towards a waterfall.
Olive is reading a romance novel and munching on a gift box of candy from Bluto when Popeye drops by. She's too absorbed to notice him, so he feigns illness. The doctors are at a loss for a cure.
When Popeye takes the baby for a walk in the stroller, the little one won't be quiet unless he's sleeping. Of course there's no end of noisiness.
Pierre Bluto, running a logging camp, has thrown Olive into the river because he didn't like her spinach. Popeye rescues her and proceeds to beat Bluto in a lumberjack contest.
Bluto dirties all of an office building's windows himself, to drum up business for his window cleaning service. When he gets to Olive's stenographer office, about ten floors up, she says no: Popeye's going to wash her windows. And the battle with Popeye is on.
It's the middle ages (sort of); Popeye is working in Bluto's Beanery. Bluto is going to the ball where Princess Olive will choose her mate. Popeye's fairy godpappy appears and it's a reverse Cinderella story, with a car created from a can of spinach.
Popeye and Bluto pick up Olive to celebrate New Year's Eve with them. Popeye brings along her granny out of sympathy.
Popeye is leaving on his sailing ship, much to Olive's chagrin. She ends up accidentally stowing away in a trunk. Popeye discovers her, but she can't stay, because the crew will think she's a jinx. She tries to hide, but this only scares the crew more, because they think the ship's haunted. When she is revealed, the crew comes after her to throw her off, and then turns on captain Popeye.
Olive has a small leak in a pipe; she makes the mistake of calling Wimpy to fix it, and the even bigger mistake of asking Popeye to help her do something until Wimpy can arrive. Meanwhile, Wimpy keeps realizing he's forgotten his tools, his gloves, etc. and going back. Popeye finally eats his spinach and manages some fixes to the system.
Olive takes Popeye to Professor Bluteau to learn some manners.
Popeye is having a dream. In it, Bluto interupts his and Olive's flirtations with one another and keeps having the upper hand.
Popeye's ensemble is rehearsing the opening of the Poet and Peasant Overture (with interpolations of the Popeye theme and "I've Been Working on the Railroad"). Maestro Bluto drops in from next door to conduct and play violin and show Popeye up. Popeye plays horribly until he unlocks the previously unexplored artistic benefits of spinach.
Popeye is wooing Olive on the phone when Bluto comes over. He overhears, taps into the line, and impersonates Popeye. They proceed to have a high-wire fight on the telephone lines outside Olive's house.
Olive is moving out of her apartment; she's hired Bluto to move her things, but Popeye comes over to visit and won't be shown up.
Olive preaches the need for brotherly love on the radio. Popeye, hearing this, does a number of good deeds: helping two workmen raise a safe, straightening a wrecked car, and helping two boys sneak into a baseball game. But when he tries to break up a fight, it's more than he can handle alone. Olive and her followers come along and try to help, but it's too much for them, too. Of course, once Popeye has his spinach...