Oral history is a research process for recording oral tradition, which is information passed verbally through generations of a community without being recorded into media. Wikipedia treats oral history as it does with any other primary source. See: WP:RS and WP:OR. Sources have to be written to be citable and verifiable.
There is no system in Wikipedia for citing unpublished oral tradition, just as neither Wikipedia nor any other research publication will cite unrecorded statements from unknown people or organizations. Anyone is welcome to convert oral tradition into an oral history, perhaps by publishing in Wikiversity, and cite that history in Wikipedia. The closer that an oral history comes to complying with the established scholarly tradition of producing oral histories, the better the source becomes for Wikipedia and knowledge preservation.