What are the methods for validating an exclusively 'oral' tradition? eg: If reference sheet music and/or audio recordings do exist, how does one parse/quantify their influence on the evolution/transmission of the song under study?

It's wise to be very wary before describing any musical tradition as exclusively oral, but the main reason for that is the existence (in huge numbers) of printed copies of the texts from at least as far back as the 17th century. However, these were scarcely ever provided with sheet music, and there's no evidence that singers (as opposed to instrumentalists) would have been able to read it anyway. It's also wise to be aware of the possible effects of broadcast or recorded music on singing tradition, but Sharp's collection and others of the period predated that development.