Almost any work of literature can be analyzed according to any literary theory. If a work has male characters in it, you can discuss male privilege. If it has female characters, you can discuss how the women are affected by patriarchy. For class or race, again you can look at the dominant class in terms of how they enact privilege and the subaltern in terms of oppression.
In general, you want to focus on some specific theme, period, genre, or group of people. For example, if you wanted to analyze gender in twentieth century Canadian short fiction, you would look at the stories of Alice Munro; "Who Do You Think You Are?" is one of the best known on that theme. Many of Margaret Atwood's poems, such as "Siren Song", also address gender.
For poems about race, the Harlem Renaissance provides many obvious examples, including "A Dream Deferred" by Langston Hughes and "A Brown Girl Dead" by Countee Cullen.
For class issues, two loosely affiliated British literary movements, the "Angry Young Men" and "The Movement" focus on the aspirations of the lower middle classes and the conflicts they experience in the highly stratified society of post-World War II England. For fiction about class issues, you might use "The Loneliness of the Long Distance Runner" by Alan Sillitoe. Philip Larkin's poetry also frequently addresses issues of social class; some well-known examples include "High Windows", "Mr. Bleaney" and "Toads Revisited".