I'm assuming that the purpose of the oil is to make the other
product stick to the plant - correct?

The oil im speaking of is usually petroleum oil or ultra-fine oil. The product
you should look for is all seasons oil, or horticultural oil. It works great
on aphids and is not particularly dangerous as long as you use it correctly. I
dont know about using vegetable oil, it seems like it is probably too heavy for
use during the growing season.

Toad