This will be really very easy. Prepare a directory you wish to extract the soundbites to, open AFS explorer, point it at <steam install directory>/steamapps/common/Jet Set Radio/DATA/JETRADIO/SND_DJTALK.AFS and open sesame!

When inside, highlight ALL the files in the right hand pane, right click, select 'Export', point that at the place you want his nuggets of funk to be dropped, click OK, and feel them slide right into your brain! JET SET RADIO!

I'm sorry this guide is so brief but that's really all there is to it! You might want to convert these to MP3 but that's something I know an intelligent computer user like yourself can handle. I'll not use the proceeding space for anything other than contemplation. Go on, go do!