Surprised it wasn't Extra, Extra Virgin Olive oil??? I've been told the holy water is just ordinary tap water that's had the hell boiled out of it.
My impression is that the power comes from Christ and garnered via the faith of others, but nonetheless He is the power which gives reason for fallen spirits to depart from possessions of other persons. The issue isn't as superstitious, as much as it is supernatural.
And your impressions are generally correct. I've had it satisfactorily explained to me by an old Franciscan as follows...
Faith is the suspension of logic...To truly believe that a man can have nails pounded through his wrists and ankles, after have been severely lashed, bled severely from the head as the result of of a helmet of thorns, then woke up three days later, as though nothing is wrong, is to suspend logic. GOD has blessed us with logic, which in a sense, seperates us from the animals, and makes us unique as humans. In comprehending HIS greatness, we must be able to suspend that logic, and therefore, there are signs, symbols, and miracles, that help us to do so. The Catholic Church is rife with symbology.