How can I stop my old broken phone getting my text messages? My iPhone cracked its screen and presently i cannot get past the locked access screen.  Got a new phone but the old phone continues to show me my new text messages.  I cannot get into old phone to change any settings.  Anything else I can do?
You can erase your older device.

Since you cannot access its settings, you can put it into recovery mode and restore it via iTunes. 

That'll erase all the content off the iPhone and as long as you don't setup your Apple ID on the device, you shouldn't receive  iMessages anymore.