I owe taxes from a few years ago that I still haven’t paid, can I file my taxes from last year today even though I still haven’t paid?

Sure, you can file your 2023 return even though you owe past taxes.

They may keep your Refund (if you are getting one) to apply to your back taxes, if you aren't current with a repayment plan with the IRS. 

Here's more info on What to Do if I Owe Tax But Can't Pay you may find helpful. 

Yes, you can file a 2023 tax return.  Understand that if you still owe back tax from an earlier year, the IRS will seize your 2023 refund to pay the tax owed.  They will take as much. -- or all -- of it as needed to pay the amount you owe.   If you have owed for several years, it has been incurring interest owed too.