In the Simpsons episode, "Homer's Barbershop Quartet," Homer tells the family about he time he, Apu, Skinner and Barney were in a successful barbershop group, and of the group's eventual downfall. Much of the story is based around the Beatles, and there's references to the Fab Four throughout the episode.
#5. After arriving in New York City, the Be Sharps hold a press conference just as The Beatles did upon coming to America:
Reporter: I have a question for Apu de Beaumarchais. Isn't it true that you're really an Indian?
Apu: By the many arms of Vishnu, I swear it is a lie.
Reporter: Barney! How did you join the group?
Barney: They found me on the men's room floor.
[Everyone laughs, but a tear rolls down Barney's cheek]
Reporter: Principal Skinner, you've been referred to as "the funny one." Is that reputation justified?
Skinner: [seriously] Yes. Yes, it is.
#4. This interaction:
Skinner: Only one question remains, gentlemen...what do we call ourselves?
Nigel: How about, "Handsome Homer Simpson Plus Three?"
Barney: I like it!
Apu: Wait, I do not.
Skinner: Er, um, we need a name that's witty at first, but that seems less funny each time you hear it.
Apu: How about, "The Be Sharps?"
[Everyone laughs loud at first, then less, then the laughter tapers off]
#3. Just as Brian Epstein tells John Lennon to not let the fans know he's married, so to does the Be Sharps manager, Nigel, tell this to Homer:
Homer: Wait till I tell Marge!
Nigel: Oh, yes...Bouffant Betty. Well, I would prefer if we kept your marriage a secret. You see, a lot of women are going to want to have with you, and, er, we want them to think they can.
Homer: Well, if I explain it to Marge that way, I'm sure she'll understand
[scene change to the Simpson home]
Marge: [cries loudly]
Homer: C'mon, honey! It'll only be until we finish our tour of Sweden.
#2. One of the greatest lines in Simpsons history:
Lisa: I can't believe you're not still popular.
Bart: What'd you do? Screw up like the Beatles and say you were bigger than Jesus?
Homer: All the time! That was the title of our second album.
#1. "Where'd you get that brownie?!?" and "It's Been Done."
This is in the episode and has nothing to do with The Beatles, but it's hilarious:
Barney: David Crosby? You're my hero!
David: Oh, you like my music?
Barney: [Surprised] You're a musician?
(Different episode, but here's a clip about Marge's obsession with Ringo Starr)