This essay by Scott Miller offers a very useful analysis of the musical and an explanation of its many influences.
One inspiration for Urinetown is the theatrical style of German playwright and director Bertold Brecht. Brecht developed the style of “Epic Theatre”. In this style, actors were not focused on being realistic, but instead, each character focused on representing a different side of an argument. Brecht used plaques, signs, songs, and narration to create a sense of detachment between the audience and characters. He thought that any connection between the audience members and characters would cause the audience to think passively. He wanted the audience to stay alert and rational, focusing on the political and social aspects of the story and leaving the theater with a want to fix those problems in society.
A good preliminary introduction to Brecht the playwright, and Brecht's distinctive approach to theater, is the video embedded here from "Crash Course: Theater." Though corny at times, this is quite a good overview of what Brechtian theatre is all about.
Other resources on Brecht:
One of Brecht's most famous works, and one that is often linked with Urinetown, is the 1929 "play with music," The Threepenny Opera.
Here's the best short summary of The Threepenny Opera that I could find: Drama And Theatre - The Threepenny Opera
Here's an interesting blog post on The Threepenny Opera that mentions its influence on Urinetown: The Bad Boy of Musical Theatre: Threepenny! (newlinetheatre.blogspot.com)
Another musical often linked with Urinetown is Mark Blitzstein's 1937 musical The Cradle Will Rock, written and performed during the Great Depression.
For more information and a plot summary, see the page on the musical at Mark Blitzstein's official website.
Here's another great overview of the musical from Smithsonian Music.
The story of how this musical was produced, despite being shut down, during the Federal Theatre Project is told in the 1999 film The Cradle Will Rock (which we screened on campus earlier this semester).
Agitprop Theatre originated in Russia and Germany as propaganda for issues like class struggle, workers rights, and capitalism. This type of theater uses simplified settings to carry complex political messages to a variety of audience members. Its use of satire and humor critiques societal norms and exposes capitalist systems. They used stereotypes or caricatures, and simple props like boxes that served varieties of purpose. They broke the barrier between audience and performer.