Are Fed and State returns submitted at 11pm 7/14/20 late?

federal is due by midnight on 7/15/2020. if it's submitted on or before that date you get a few extra days to correct and refile.  you didn't mention which state.  some did not extend their usual due date so now it could be late. 

I fell asleep and missed the 7/15/2020 deadline.  (Really!). I'll pay the penalty, etc., but I can't see a way to file.  What do I do?

I get it that I'm late, both for the federal and state returns.  (West Virginia). My question is how can I file?  Does the turbotax allow for later filing, or do I have to file by regular mail?

E-filing remains open until October 15, 2020.

If you are getting a refund, there is not a penalty for filing past the deadline.  If you owe taxes, the interest/penalties will be calculated by the IRS based on how much you owe and when they receive your return and payment. The IRS will bill you for this; it will not be calculated by TurboTax.