This could certainly be accomplished using a Web Service and a Web Part.
Can you ask a more specific question?

To be more specific here is how it works. Right now we can set  up a
email account that connects to our local phone  system. The only
settings that matter is the incoming IMAP and Outgoing SMTP are set to
the IP address of the phone system  192.168.1.15

Then we just enter the username of our extension and the password of
our voicemail password. Then anytime we get a voicemail they are
downloaded to our outlook. We can then click on the email and
attached in it is a wav file.

I would like to figure out how I could have a little web  part that
each person can configure with their username and password and it will
allow them to open these messages from sharepoint.