This is an interesting question and one not easily answered, I think. Oates structures her story so that Zachary's struggle is witnessed through an observer's experience while the narrator tells about the witness. The narrator is limited third person. From time to time, Oates changes the character through whom the narrator is limited. Most often the narrator is limited through Sunny. This means that, at these times, the narrator sees into Sunny's actions, perceptions, and thoughts. Other times, the narrator's focus shifts and is limited by Zachary's experience, perceptions, and thoughts:
He'd bought the ring at Stern's Jewelers, ...How astonished, upset, furious his parents would be when they learned--Zachary hadn't allowed himself to contemplate.
While the narrator occasionally tells us directly about Zachary, as above, we most often learn about him through Sunny. This discussion of the narrator is significant to the question of who is the protagonist because most often a limited narrator stays with the protagonist.
The fact that there is a shift underscores the idea that the protagonist is actually Zachary and his story is twice being told, first by Sunny's experiences with and reactions to him and second by the narrator. Sunny appears weak as the protagonist because her life outside of her involvement with Zachary is told in broad strokes, without in-depth detail. Only when Zachary enters her life, either directly or indirectly, does Oates provide details--and the details all tend toward enlightening Zachary's experience of his life.
While the protagonist may be debatably Zachary or Sunny--or both--the antagonist is easier to identify. In the struggle of human against society, society is the antagonist. Tobias makes it clear in the protracted titular epilogue that Zachary was confused, torn, conflicted by his place and his role in society:
[Tobias] passed his hands over his eyes. "I couldn't have loved Zachary .... But I could have allowed him to know that he wasn't sick, crazy, 'perverted' as he called himself in that letter. ... I could have made him feel less lonely. ... My only friend."
Zachary didn't understand how society worked, nor did he understand how he might work within the mechanism of society. This all meant that he had no way of understanding himself since our first knowledge of ourselves comes as a reflection from society's reaction to us. This is exactly mirrored in Oates structure: we know Zachary's story because of Sunny's reactions to his entry into her life.