Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person (Omniscient)
"Her." "They." "She." All of these words along with the complete absence of an "I" voice indicate that Strega Nona is written in the third person. We know from the start that we're getting this story from an observer who isn't involved in the action—a narrator who is outside looking in—and that's the classic definition of a third person point of view.
As for the omniscient part, we have to dig a little deeper to get that. We see that the narrator knows Big Anthony's thoughts and feelings when we of his anger over being laughed at and hear the words he speaks to himself (14). We also know and what he's thinking when Strega Nona leaves: "My chance has come" (15)! For a while, though, it seems like maybe Big Anthony is the only character the narrator is tied closely to, which would make the point of view third person, Limited Omniscient. The thoughts and feelings of other characters are, for the most part, communicated by actions which would be easily observable by anyone.
But when the pasta tsunami hits, we learn that "the townspeople began to worry" (25), which represents the internal feelings of lots of folks. And when Strega Nona returns in the midst of the chaos, we are told, "She didn't have to twice to know what had happened" (29). That, too, is an internal thought, and since the narrator knows what all these folks are thinking and feeling, we know the narrator is omniscient, and that the omniscience is not limited at all. Boo-yah!