Though I have been interested in mysticism and all things occult for a long time (it all probably stated with The Tao of Physics), it took my discovering John Michael Greer's writings--in particular, his Well of Galabes blog--to acknowledge to myself that there is something over and beyond what can be explained by science and sensed by us through our, well, senses.
I can't really point to any single extraordinary incident that tipped me over to the other side, so to speak, it's more of a retrospective 'audit' of the things that happened over the last week, month, year, and so on, an audit that reveals interesting patterns, a balancing or settling of accounts if you will. Karma and cause and effect and all that.
Anyway, at the risk of sounding woo and cryptic, let me just say that the phrase 'Change in consciousness according to will' seems to be a good place to start.
Oh, and I have my own banishing ritual now, based on the pantheon of our deities.
To take the original thought that kicked off this post to its conclusion: the elderly catholic woman, in all probability, reaped the same benefits that she would have reaped had she been praying to a statue of the actually-intended saint. And no, I don't mean this in a facetious sense.
P.S. Reddit has an occult sub. Don't forget to check out the Illustrated Beginners Guide to Chaos Magic.