I think worrying about dating your work is pointless. Every last work anyone writes is going to be easily dated, even if it's set five thousand years in the furtue. You can read any novel and have a very good idea exactly when it was written, and any novel set in the modern world is easy to date.
And if you could somehow mangage not to include naything that would date your work, it would float in nowhere, neverwhere, and probably be a lousy book.
It's your writing style you want to keep dateless so poeple can still easily and pleasurably read your work in fifty or a hundred years.
But you will not and cannot stop your work from being dated, and shouldn't want to. I don;t know where the idea comes form that dating your work is bad. It sure hasn't harmed the hundred and thousands of dated novels that have been around for anywhere from decades to centuries.
Anyway, you can use titles of songs, and you can use a lyric from a song as a title. Just don't use lyrics themselves in teh body of your work.