First of all, get the QuickTime Player; yep nobody loves it, but we can't play the files without their wonderful codecs. Then, in order to:
Play the AMR files using Winamp:
Download and install MediaLooks QuickTime DirectShow Source Filter.
It is a DirectShow filter, so, after installation, run Winamp > Options > Preferences > Plugins > Input > Nullsoft DirectShow Decoder.
Click on Configure button and add ;AMR to the extension list.
Play the files using Windows Media Player:
Downloa and install River Past QuickTime DirectShow Filter for WMP.