The title is a play on the 1982 film Poltergeist.
Daffy Duck and Porky Pig deliver a package to a haunted hotel, the Terror Inn, in the middle of a spooky storm. Porky wants to wait until the next day, or leave entirely, whenever he's spooked by lightning or ghosts, but Daffy insists on pressing on regardless. They arrive at the inn, where Daffy uses a powerful air horn to get the attention of the residents to be allowed in. This angers the slumbering ghost within, Norm Macabre, who allows them inside to get his revenge.
While Daffy looks for a phone to contact the inn's service, the ghost blasts Porky with a bunch of letters, which get stuck in his ears and eyes and mouth. Daffy continues undaunted to the broken elevator. While Daffy tries to fix it, Porky is once again tormented by the ghost, animating nearby plants to strangle him and reshape him into a pretzel until Daffy fixes the elevator. Porky meekly protests, but Daffy has them continue into the elevator.
The ghost hits multiple buttons, and on each floor a new horror is seen by Porky Pig, some reaching in to attack him, while Daffy is distracted by a penny. When Daffy finally sees the same ghosts Porky does, he ignores them, telling them to eat more vitamins as he marches onto the floor where the package is to be delivered. As they walk, Porky notices that all the paintings on the wall are of dead pigs, and when he finally sees floating candles, he snaps and tries to run away. Daffy stops him, reassuring him that "there's no such thing as ghosts."
As Daffy leans against a suit of armor, the sword is dropped by the ghost, slicing off his bill and half the feathers on his body. Finally seeing the ghost, Daffy and Porky both run in terror. They land on a wheeled rack which slides down the hallway via their momentum, with the pursuing suit of armor hacking it apart underneath them. They and the suit of armor eventually crash into the end of the hall at the very door where they are to deliver the package.
A demonic horror emerges from the room and terrifies the pair, with Daffy shaking as he presents the package, addressed to Mr. Macabre. Seeing this, the monstrosity transforms back into his usual ghostly self, apologizing for scaring them since he forgot that he ordered a package last week. He offers them gold as a tip, which excites Daffy and Porky; however, the gold is ghostly as well, and immaterial, falling through their hands as they try to catch it. Macabre then finishes with the saying, "easy come, easy ghost."