I would also add that a major conflict is fate vs. free will--in this case, at it relates to the "fuku," the supposed curse on the family and Dominicans in general. Oscar's quest to be loved and to be redeemed comes into conflict with several forces--American society, his past, Dominican gangsters--that challenge his ability to live the life he aspires to.
One other subcurrent is the narrator, who must come to grips with Oscar's actions and his relationship to Lola and the rest of Oscar and Lola's family.
There are two conflicts primarily present in this story. The first one is man vs. society. From Oscar's family history in the Dominican Republic, readers learn that discriminatory behavior towards the family is the cause of many of their problems. Beli's sisters were killed by a totalitarian leader. Beli herself was ostracized for her appearance and then beaten by the same totalitarian leader. In New Jersey, the family suffers from a lack of acceptance due to their cultural background, leaving Oscar to feel alienated and unloved. Society has put undue pressure on the characters.
However, at the true heart of the story, is a man vs. self conflict. Diaz focuses less on this issue of society in her narration, and more on the reactionary behavior of the characters. These characters make bad decisions based on their needs and suffer as a result. Beli and Oscar both want acceptance so badly that they get invovled in dangerous and forbidden relationships. If they reacted more positively to their needs, each character would have experienced a less brutal life line.