Hi John,
I think it depends on how large these audio files are-- if they are small enough, I wouldn't worry about having them stream in the technical sense of the term. With broadband as fast as it is, I would just use the HTML5 audio or other embed tag and point to them. Files can even begin to play without being fully downloaded in the player. A lot of "streaming" music services behave this way.
The advantage with true streaming is the ability to take huge files (think of a Netflix or HD YouTube video) and jump to any part of the file without the whole thing having to download. It's also essential, of course, for delivering live content.
On another note, the HTML5 audio tag can support multiple sources of content, and if you have both an AIFF and MP3 version of the file on your server, the tag can be written to prioritize the AIFF while having a redundant playback option for MP3 for larger support.
Anyway, this is my understanding of the issue, from working on software for our language faculty. Best of luck!
Dan Nickolai, Ph.D.
Director of the Language Resource Center
Department of Languages, Literatures, and Cultures
Saint Louis University
(314) 977-3644