What components can introduce a hum to a circuit?

[antonis]

So it stands to reason the effect is amplifying the inherent hum in a manner that is being exaggerated by self oscillation.

Hum is low frequency "interference" and for a "normal" op-amp can't result in self oscillation by itself..
(at hum freq, phase difference between Out & In is almost 180^o which is FAR AWAY from the unity gain point..)