Q: Deleted voice mails keep reappearing and keep voice mail full

Hello, TracyG329. 

Thank you for visiting Apple Support Communities.

Try forcing all applications to close and power cycling the device.  Test accessing and deleting unwanted voicemail messages.  If the issue persists, try the steps in the second article below.

iOS: Force an app to close

http://support.apple.com/kb/ht5137

iPhone: Troubleshooting voicemail

http://support.apple.com/kb/TS4430

Cheers,

Jason H.