Many different critical approaches can be used to examine A Clockwork Orange. Because of it’s complex polyglot style, it can be said to function as a bricolage. This sort of composition lends itself to analysis based either on dialogism or ludic postmodernism.
If you are most interested in the dialogic and carnivalesque aspects of the novel, you might want to start with the critical theories of Mikhail Bakhtin, whose work would enable you to foreground both the multiple voices and class structures of the novel.
If the humorous characteristics of the work attract you, ludic postmodernisms such as that of Lyotard might be a good theoretical frame.