Homer begins challenging everyone around him to duels after he sees a Zorro film at the Googolplex. Most people back down, until Homer meets an old-fashioned Colonel who takes him up on his dare. Unable to get out of the contest with the Colonel, Homer and his family flee to the country, where they become farmers. Farm life is difficult until Homer creates a new crop called tomacco—tomatoes crossed with tobacco.
The Simpsons go to a movie theater to see The Poke of Zorro. Afterwards Homer, imitating Zorro, frightens Snake away by challenging him to a duel, slapping him with a glove. He starts to use his dueling glove to get anything he wants from people: First up is Moe, for calling him "heavyset", but after a slap, he gives Homer a free beer. Thus begins a montage to the tune Glove Slap a parody of The B-52's song "Love Shack". When a gun-toting, Southern colonel actually accepts Homer's challenge, Homer finds himself bound to a duel at dawn the following day. Later that night, the family assure that the colonel won't show up and Bart insulted Homer. Homer was about to hit Bart to challenge him to a duel; however, his family stares at him because he didn't learn his lesson. The next day, the colonel shows up, they sneak out with Homer clinging to an old Christmas tree and search for a temporary home. The colonel and his wife set up camp outside the house in his RV, awaiting the duel.
With Homer fearing for his life, the family sneak out—by hiding Homer behind a Christmas tree—and search for a temporary home. Along the way they spy Jimmy Carter's Habitat for Humanity: Homer calls Carter a lazy bum, who responds by pulling off his glove to slap him, as Homer has been doing. Homer drives before Carter has a chance to slap him. They find Grampa's old farmhouse on Rural Route 9 outside of Springfield, where they decide to live and, despite the land's poor reputation for growing crops, Homer becomes a farmer.
Homer calls Lenny and requests that he send plutonium to make the crops grow "real big, real fast". They do eventually grow, but since Homer scattered seeds indiscriminately, his main crop is Tomacco, a mix of tomato and tobacco, which tastes bitter but is very addictive. It is such a success that executives from Laramie Cigarettes offer to buy the rights to Tomacco for $150 million.
Homer rejects the offer as insulting, demanding $150 billion for tomacco, which they refuse to pay. Dumped back at the farmhouse, the family see tomacco-addicted animals from other farms eating their crops. Homer saves the last plant, but when the rest of the animals attack the house, he tosses it into the air and it lands right into the hands of a Laramie executive.
The Laramie executives' helicopter leaves, but a tomacco-addicted sheep has snuck on board. It creates mayhem, causing the helicopter to fly out of control and crash, destroying the final tomacco plant and killing everyone onboard (though the sheep is shown to survive). With all the tomacco crops gone, the Simpsons return to Springfield, forgetting that the Colonel is still there. The Colonel shoots Homer in the arm, but Homer says he will only go to the hospital after having some of Marge's mincemeat pie.
NOTE: This episode creates a plot hole in the previous episode, "Grampa vs. Sexual Inadequacy", where the farm house was burned down by Homer and Abe. The only possible explanation is that "E-I-E-I (Annoyed Grunt)" takes place before "Grampa vs. Sexual Inadequacy" or the house was saved or rebuilt and ended up back to it's previous state.