Copy voice messages from iPhone
Try this app - http://www.ecamm.com/mac/phoneview/

It copies all the info you mentioned to a Mac. Free trial to be sure you like it before paying.

If this is one time (or your value of the time it takes to manually record these is less than $30), just hook a stereo plug from the phone to the computer and record the mic input on the Mac. (Or PC if you use that computer)