The title of the episode is based on a FOX ad campaign at the time, where "Da Boom" was supposed to be Jamaican slang for the best, or cool.
When Stewie breaks under the pressure of the Griffins' exodus, he says "Game over, man. Game over!" like the character "Hudson" does in Aliens.
When the family is on their way to find the Twinkie Factory, they come across a house in a green area. This is a reference to the short lived Fox series Woops!
Awestruck by the Twinkie factory, Peter parodies the movie Contact, saying "No words...should have sent...a poet..."
Stewie, as a mutant, climbs onto the ceiling declaring he is Fred Astaire, the actor/dancer. Specifically, he is referring to "You're All the World to Me", one of Astaire's most memorable dances, from the film Royal Wedding. In it, a rotating room was used to enable Astaire to dance on the ceiling.
When Peter's orders for guns have been met, he holds a hand gun while saying "A chicken in every pot, and a cap in every ass," referring to Herbert Hoover's 1928 campaign slogan "A chicken in every pot, and a car in every garage."
Peter's line, "When the end of the world happens you'll have to meet those two dead bailiff ladies from Night Court, and you won't know which is which, and it will be really awkward, so bite me!" is a reference to actresses Selma Diamond and Florence Halop, who died in 1985 and 1986, respectively.
In the scene in which the family is walking to Natick, Lois tries to get Chris to stop saying "Left foot, right foot" by saying "Stopiiiiiit!" This is similar to Ferris Bueller's Day Off when Jean tries to stop her mother from yelling at her while she's driving.
Victoria Principal and Patrick Duffy's appearance at the end refers to the famous "it was all a dream" sequence on Dallas.