I think that at the time this became a treatment the only available oil was olive. I do not remember seeing sunflower or vegetable oil freely available when I was a kid. Having said that, hydrogen peroxide (very cheap) diluted in a small egg cup of warm water is much more effective.
I suppose olive oil is a traditional remedy and I remember having it poured at just above blood heat into my ear as a kid many years ago. Cannot see why a clean pure vegetable oil wont do, especially if you add a drop of tea tree oil which is a gentle antiseptic.
I reckon many decdes ago someone had boobed and bought loads of low quality olive oil. Desperate to offload it, no one in the UK would touch it for consumption. Then someone said, "I know, why don't we try to get folk to shove it down their earhole ?", and the rest is history.
It makes me laugh when I think of all the types of olive oil you can buy in the supermarket, yet when I was a child you bought it in a miniscule bottle from the chemist