Q: Reset iPhone that runs with an old email and password for my Apple ID

If you mean you want to restore it as new, use this article: How to erase your iOS device and then set it up as a new device or restore it from backups - Apple Support

If you are unable to do so because you are logged into Settings > iCloud with the old name of your Apple ID, use this article:  If you're asked for the password to your previous Apple ID when signing out of iCloud - Apple Support

Do you mean reset or restore?

A reset does not require anything from you in regards to your Apple ID.

A restore will require you to turn off Find My iPhone first (if enabled), which will require your password.  But if this is the same Apple ID as you have now, and you've just changed the email associated with your ID (and your ID password) then use the current password to turn off Find My iPhone.  But if you have an entirely new Apple ID, then of course that won't unlock your iPhone 4's Find My iPhone -- you have to use the old ID.  If you don't remember the password for that old ID, then reset it:

If you forgot your Apple ID password - Apple Support