What part of speech is 1930s?

Depends on the sentence.

"The 1930s were the highlight of American culture." - subject, noun.

"Wow, your jeans are sooo 1930s." - predicate adjective, adjective

"I haven't partied that hard since the 1930s." - not sure, but a noun.

"How were the 1930s?" - predicate nominative, noun.