Morals vs Inner Nature
This would be the most significant theme of the novel: the inner dilemma faced when sexual desires conflict with one's moral compass. As even defined by the author: "Portnoy's Complaint: A disorder in which strongly felt ethical and altruistic impulses are perpetually warring with extreme sexual longings, often of a perverse nature." Over the course of the story, Alexander reveals his constant struggle between his ethics and his libido. While his conscious mind attempts to restrain him, he cannot help but indulge in acts judged depraved by society. It is a constant battle which he is often the loser in, for he cannot control his inner desires which burn so strongly.
Assimilation
Another less obvious theme of Portnoy's Complaint would be the assimilation experience of American Jews, and their at times strained relationships with Jews living in Israel. Alexander is a Jew living in America, and some Jewish ethical values only constrain him further.
Candidness of Sexuality
Throughout the novel, Roth is frank and open about sexuality in a practically unprecedented manner. The novel's protagonist openly admits how he indulges in masturbation, aided by completely unorthodox objects including a liver. Roth does not censor any sexual scenes (though some argue that he should have), and his absolute candidness in portraying human sexuality in all its forms is what truly distincts the novel.
