An interesting topic, especially for a high school project! A little terminology that you may or may not know - "the history of oral history" = a topic of historiography (the study of the history of history, roughly speaking).

My understanding is that oral history became more valued by the community of historians in the 1950s, with a greater interest in African history. Historians before that (and often today, as well) relied almost exclusively on textual sources. However, these were in many cases not available for pre-colonial African history. (Depending on where and when you're talking about.) Thus, Africanists helped pioneer the use of a number of alternative types of sources, including oral histories and evidence derived from anthropology and archaeology. Now, this is what my African history professor told me, so take it with a grain of salt, come to your own conclusions, but don't be surprised if it's difficult or impossible to find pre-1950s collections of oral histories of veterans. (And if you do find them, that could be quite interesting.)

I assume you're working primarily or exclusively with American military veterans? If not, there are probably other places to look, but here are some ideas. The Library of Congress seems like a good start; here is a link to some information on the Veteran's History Project there, which was apparently begun with legislation passed in 2000. There are also some links to earlier oral history collections provided here. Honestly, I would just contact a librarian working on that and ask them if and how oral history of military veterans was collected prior to the project. You can contact them here. The Library of Congress librarians that I've dealt with have been very helpful - seriously, don't be afraid to reach out to them. You might also check out the National Archives, which holds veterans' service records (and is responsible for organizing and storing all government records).

Hope this helps!

Edit: Formatting