Classics is bandied around a lot:
If someone said to you 'I'm studying Classics' or Classic era books, they'd mean things like Ancient Greek books, like the Odyssey.
If someone said to you 'You need to read some classics', or we were talking about Classic literature,or 'the' classics that would be anything before 1900 which is still in print. 'Jane Eyre' is a classic.
Anything after that is considered a modern classic, although people often call them classics. Of Mice and Men is certainly a classic. For 20th century literature most people like to call anything they liked reading a 'classic'.
A sub-genre of modern classics is 'cult literature'. This means anything that has become popular enough to have followers, and often gain popularity after having had a film about them. 'The Beach' is considered 'cult literature'.
You've named a lot of modern American classics in your answer, so may I add?
The Great Gatsby- Scott Fitzgerald
Tender is The Night- Scott Fitzgerald
As I Lay Dying- William Faulkner
The Sun Also Rises- Ernest Hemingway
Lolita- Vladimir Nabokov
Bonfire of The Vanities- Tom Wolfe
1984 is definitely worth a read! And seeing as you liked Catcher in the Rye, perhaps you might like 'A Clockwork Orange' by Anthony Burgess?