Voicemail transcription

You cannot turn off transcription. However, it's unlikely that is the cause of your problem. Are you able to listen to your messages if you call into your voice mail directly? You should be able to do this by dialing your own phone number. What you do after that may depend on your carrier. For my carrier, you interrupt the greeting with the # and enter the passcode. I can also dial in using the short code *VM. However, contact your carrier for instructions (and a reset of your passcode if you've forgotten it).

I'd suggest you then clear out your voicemail. Once that's done, see how it works from the Phone app.

If that doesn't work, have your carrier reset your voicemail.