I have two phones. My old Apple ID was deleted but is still logged in to one of my phones. I can not delete or remove the old Apple ID to create a new one for this phone.

If you did not sign out that AppleID on the device before you asked Apple to delete it, then it is a brick now, as explained in the documentation you read when requesting the AppleID be deleted. Apple will not be able to do anything for you now that the AppleID has been deleted.

It is very important when asking for an AppleID to be deleted to follow the directions explicitly. Once the AppleID is deleted, there is nothing anyone can do about it if it was still signed in on any device.

How to delete your Apple ID account - Apple Support

• “Make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted.“

If you are the original owner, contact Apple. Apple may be able to remove the Activation Lock if provided the required paperwork. Since the ID was deleted, they may not be able to help. Either take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store (if it has reopened)

Genius Bar Reservation and Apple Support Options - Apple.    

or contact Apple ID Support. 

 Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.  (Link doesn’t always load)   

Get Support      Work through the screens to get a chat option. 

Apple Support schedule phone call

https://twitter.com/AppleSupport       People have posted it may take an hour or more to get a response.