Updike's style is derived mainly from irony and humor.
The story is told from Sammy's point-of-view, so we hear his teenage vernacular and sarcasm. Clearly, Sammy sides with the girls and resents adult authority figures. Since he tries to be the hero in his own story, we empathize with him, even after he is fired and fails to impress the ladies.
Sammy uses much grocery store metaphors and imagery, especially as it pertains to the female shoppers. People and products have become confused in the materialistic and commercial world of the A & P. Just listen:
...just come from between the two smoothest scoops of vanilla I had ever known."
Since Sammie's framing his story from one vantage point, he's an observer-narrator. He mainly comments on the cultural differences between the adult and pre-adult world. The A&P is an adult world, with neat aisles and shelves and prices. When a group of teenage girls intrude on that world, it makes the adults look crass, conservative, and materialistic. By the end, Sammy rebels against the adult world, but he knows he can't survive without it for long.
I think one of the most prominent style elements in this short story is the way point-of-view creates such a specific tone. The story is told from the perspective of the checker, Sammy. First, Sammy is not much older than the girls who come into the store that day. Likewise, he is a male who is physically stimulated by the fact that they are wearing bathing suits.
Keeping those things in mind, as a narrator, Sammy's voice (tone) comes across as overly "cool" about the entire incident, almost as if he is forcing apathy. While older women in the store decidely stare in criticism, Sammy tells the story like it was no big deal. In this way, he can take the girls' side pragmatically, as a matter of principle, rather than looking just as immature as they do.