Morty Jr does a reenactment of the scene of Kevin Bacon from Footloose [1984].
The giant stone head that rains sex robots is a reference to the cult science fiction show "Zardoz" (1974) starring Sean Connery and written and directed by John Boorman.
On the steps to the queen's throne are the words "Sis Semper Calumniam". This translates from Latin as roughly "You always oppress me".
The sex robots are patterned after the "Sexy Robot" character created by and popularized in the paintings of Japanese commercial artist Hajime Sorayama.
Although the title and plot of 'Raising Gazorpazorp' are in reference to Raising Hope (2010), its creator Gregory Thomas Garcia has stated that he borrowed the show's title and concept from the influential 1987 cult film Raising Arizona (1987) by the Coen Bros (directors of Fargo (1996), The Big Lebowski (1998), No Country for Old Men (2007), etc.), which is about an unusual family facing an unexpected baby.