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 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 Bluto stop by to see Olive and fix her leaky faucet. Popeye does it better, and Bluto gets jealous, so he starts rerouting Olive's plumbing and causing all sorts of leaks.

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.

Bluto is the boxing champ, Popeye his challenger, Wimpy the timekeeper. Popeye is pounded mercilessly until Olive comes by with a can of spinach.

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.

In Judge Wimpy's courtroom, Bluto accuses Popeye of assault and battery; he claims to have been attacked by him on several occasions, without provocation. Popeye then tells his side.

Popeye and Bluto are, believe it or not, pals and partners in a moving company. (Maybe it's because Popeye isn't squinting here.) Anyhow, Olive has made the mistake of hiring them. She hasn't finished packing yet, so the boys, smitten as soon as she answers the door, compete to help her. Once packed, they compete to move more impressive piles of her belongings. Popeye easily wins these contests, even though Bluto locks him in the van at one point. At the end, Bluto socks Popeye into the piano, then into a table; though he hardly seems to need it, Popeye still eats his spinach, then thrashes Bluto.

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 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.