One of the men that dig up The Ghoul uses a Junk Jet, a weapon from the Fallout games that is essentially a steam-powered potato gun, literally shooting whatever junk items you're carrying.
Overseer Hank calls Lucy "my little sugar bomb." Sugar bombs are a brand of cereal in the Fallout series.
Lucy uses a stimpak on her wound that makes the exact same sound as in the Fallout games.
The names of the three main characters are revealed by on-screen titles soon after every character is introduced. This is a nod to The Good, the Bad and the Ugly (1966), where the titular characters are introduced in a similar fashion. Said film is also referenced a few times in Fallout 2: A Post-Nuclear Role-Playing Game (1998).
The futuristic red car displayed at the end of the birthday party scene is the 1960 Plymouth XNR prototype.