Situational Irony: Sexual Education
Feldman was expected to marry a man and ultimately have children (which involves sex), yet she was not allowed sexual education, something which would have helped her marriage and her mandate to have kids.
Dramatic Irony: Feldman's Attraction to Germany
Readers know that Feldman's grandmother survived many concentration camps in Poland and Germany. Feldman, however, does not know this and has a fascination with Germany (she eventually moves there), a place which once worked to destroy her religion and its adherents.
Situational Irony: Education
In Feldman's community, despite the fact that they are looked down upon as inferior beings, women are much better-educated than their male counterparts because of the fact that females are unable to study parts of the Torah.
Situational Irony: English
The community which Feldman and many others lived in was in the United States, a country of mostly English speakers. However, Feldman and other inhabitants of the community were essentially barred from reading and (mostly) conversing in English.
Verbal Irony: Happiness
Oftentimes, Feldman outwardly expresses her happiness in living in the community. Yet, she is planning her escape.