The Diving Bell and the Butterball - Homer is paralyzed by a spider bite, but can still communicate...through flatulence.
Dial D for Diddily - Ned becomes a vigilante by night.
In the Na'vi - Bart and Milhouse do Avatar. Also, Homer gets his arm trapped by a boulder and has to chew it off.
When Bart, Lisa and Maggie come home from trick-or-treating, Marge switches the candy with dental hygiene products with Homer owning a bag of candy that Marge wants him to donate. Homer runs away, promising that he won't eat it. After driving many miles he reaches, "Candy-Eating Peak." He runs and climbs up it until he falls into a hole, and gets his right arm trapped under a boulder. He calls 911, who say they'll be there in 20 minutes... Not being able to wait that long, Homer actually tries to eat his arm off. He eats his left arm and leg off, then finally eats his the right arm off and opens the bag... it turns out to be vegetables with a short message from Bart and Lisa who took his candy. They are seen laughing and eating the candy. Then, the camera zooms in on Bart's candy-filled mouth, showing the episode's red title.
The Diving Bell and the Butterball
In a parody of The Diving Bell and the Butterfly, Homer is quickly paralyzed by a black widow spider and is thus unable to speak, hinting that his case is called Locked-in syndrome ... While Lisa is reading a long book to Homer, Homer tries to tell Lisa he doesn't want to listen, and starts farting repeatedly. Lisa figures out that Homer can communicate this way. Then, Homer is bitten by another spider, and turns into a superhero parodying Spider-Man. He then has a dark-blue and red costume and can now fart out spider-webs. Or as Chief Wiggum says "webs".
Dial D for Diddily
In a parody of Dexter, Ned Flanders is tricked by Homer to kill for him using a voice-warper to pose as God. Ned kills as many of Homer's enemies as possible, starting on Mr. Burns after Ned sees Mr. Burns dumping radioactive waste into a lake. Homer tells Ned to turn Mr. Burns to ashes, then pee on the ashes. Ned then cuts Mr. Burns' head off and throws it into the lake, and Mr. Burns' head then grows a third eye from the radiation in the lake... Ned also kills Sideshow Bob and Patty and Selma. Patty and Selma are lured by free cigarettes, then suddenly killed, parodying Wile E. Coyote but without failure. Ned figures out Homer made him into a killer when Homer says "Hi" to Bart. Ned then appears behind Homer. Homer starts burning Ned's Holy Bible (that he had under his arm) when suddenly the Simpson's roof is torn off and the real God chokes Homer to death. Marge comes in and asks if God can fix everything that happened, but God says the Devil wouldn't like it. Satan suddenly appears with a demonic version of Maude, it is shown that God is also under Satan's power when Satan asks for a coffee.
In the Na'vi
In a parody of Avatar, Milhouse and Bart are sent to Rigel 7 (the home planet of Kang and Kodos) while in the alien bodies of Rigellians, to retrieve a chemical called Hilarium. Bart impregnates a local inhabitant named Kamala on the way. The Hilarium is found when Kamala's parents say that Hilarium is needed for their pregnant females, or all the females will get grumpy. Then when Milhouse is shown the Hilarium accidentally, he contacts the army that sent him and Bart to Rigel 7. Later, the army attacks, but the local aliens on Rigel 7 are stronger than the humans, beating them all up. Bart finally gets rid of Superintendent Chalmers by telling him he had something on his cheek while Chalmers was inside a battle suit, causing Chalmers to hit himself and plummet off a steep cliff... Meanwhile the two aliens, Kang and Kodos, admit that they would have just given the Hilarrium to the humans anyway.
At the end, a Christmas carol is played as all of the characters (that appeared in the previous three stories) all said various things about the upcoming Christmas, such as Marge saying "Making a sweater loses 27 people their jobs". At the very end of the carol, Grampa Simpson shows up dressed in a black tutu, asking when the Black Swan movie comes up... Everyone was thinking, when the Black Swan will come.