iPhone 7
After deleting the messages from my voicemail I am still getting a recording saying the voicemail is full. I turn the phone off and turn it back on thinking that would help but still and this is a work phone
iPhone 7 Plus
Check with your carrier. They are responsible for voicemail. It is very possible there is something stuck in the server that is crating that message. They can reset your voicemail and take care of it.