There are two things you need to understand about Benedict in order to really grasp how he does what he does. The first is that Flitwick was correct; he is a nephil (plural nephilim), which is defined for the purposes of this story in the Lexicon. The second is that he's a Catholic priest. Now, the exact nature of what it means to be a nephil will be explored throughout his story and another character appearing soon in the Narrator blog, and who Benedict's biological parents are will be revealed in story. So let's focus on the second for now.
Within the Roman Catholic Church, there is a belief that people undergo a number of specific ontological changes throughout their lives of faith; that is, the very essence of who they are is altered in some way through specific sacraments, such as baptism. These changes are more or less considered permanent, as they cannot be lost but the benefits of them may be sacrificed through mortal sin. There seems to be quite a lot wrapped up in this doctrine, and since I'm not Catholic I only have so much exposure to it anyway, so the focus here is on how this affects Benedict in terms of the story. If you are interested in the actual doctrine, this website seems to be helpful.
The belief relevant here is that the ordination into priesthood makes the priest a functionary of Christ. On a spiritual level, they are united with Christ in such a way that there can be times when it is Him acting or speaking or listening. Now, whether or not this is accurate within the world of Tall Tales is somewhat irrelevant. What matters is that, whatever it is that happened to the priest, it works. They administer sacraments, they preach powerful homilies, they cast out demons, they receive confession and are able to deliver a real sense of absolution, and so on. This state of priesthood cannot be lost, but the office of priest can, in fairly extreme cases. This means that Benedict, as a priest, will always be a priest as far as the spiritual nature goes, though if the Catholic church were to reject him for some reason he would no longer be allowed to act as a priest or administer sacraments or be paid by the church or any of that.
Now, in actual Catholic doctrine, this is about as far as this goes. There is no physical change to the priest, and there was no physical change to Benedict when he became a priest. What this means for Benedict, however, is that whatever benefits he has naturally by being a nephil, he gets to keep. Those are part of his biological reality and do not change through ordination. However, spiritually, he is not a nephil, but a priest. This means that, even if a being can detect his nephil biology, if they had enough information on his spiritual nature they would encounter something very different.
Within the rules of Tall Tales, this gives priests power that they are not believed to have in the real world, at least as far as I know. Mainly, this means that when dealing with spiritual entities, they are treated as holy beings. Their blood and spit and sweat function as holy water. This is because they are already consecrated, and their bodies are being used for divine purposes, which is basically all that needs to happen to create holy water. Their spirits are resistant to demonic attack (something that I think Catholics in general would agree on). They aren't immune to magic, at least in any way comparable to Matteson, but they are protected.
So, what you see from Benedict in the story is a combination of his biological nature and his ontological nature, based on taking what the Catholic church believes about priests and just applying that to a world that operates on slightly different rules. Maybe they work because this description is accurate, or maybe they work because enough people believe they work, but for the story all that matters is that they do, in fact, work.
What is this?
Worldbuilding Wednesdays is a real-world blog, written by Tim McLaughlin, that gives a little peek behind the curtain of Tall Tales. That includes the process of creating the story and world, influences, world rules, and even the occasional story.