The parental irony
Ajay's life is shaped by irony from the get-go. His father isn't very impressive. He wants to be wealthy, but he doesn't want to work, and when they have only a little bit of money, he spends it on himself. He leaves the wife to work and take care of the house. It isn't one of those mutually beneficial arrangements where the wife works and the husband does the household work; he is exceptionally lazy and makes her do both. He then afflicts her with his authority as if to prove a point.
America as a bitter irony
The family decides that life will be better in America. They undertake a serious risk. On the one hand, America represents the possibility of new opportunity and the dream for a better future. On the other hand, once landed in America, they realize some dramatic irony was working against them. They are newcomers and foreigners in a nation with racial prejudice. The opportunities that are available to the people in their community are concealed and competitive. Ajay realizes that to become successful, he will have to work the system, perhaps leaving his family behind.
Birju's ironic twist of fate
The story of Birju seems to be heading one way and then suddenly there is an ironic reversal of fate. He starts as a type-A, dominant brother, the socially powerful brother of the two, but then after a serious injury leaves him brain-dead, the foil is reversed. Ajay's sense of inferiority becomes an ironic burden around his neck, and he realizes that if someone is going to save the family, so to speak, it will have to be him. There is no longer his brother's shadow to hide him.
Success and health
There is a dramatic irony in Ajay's burgeoning sense for success. His father is unsuccessful, but for multiple reasons. Each of those reasons can be seen as a way of improving health if a problem is addressed and fixed. Birju's stay in the hospital awakens Ajay to the issue of health, and he discovers the solution to these riddles. By working to alleviate mental health issues in his life, he can become more competent, which will make opportunities more accessible.
Alcoholism and irony
The unhealth of the father is rooted in an Oedipal desire for comfort and ease. Life isn't easy unfortunately, and that leaves the father in a chronic position of pain, which he uses alcohol to medicate. This is an ironic problem because it accelerates his incompetence, and it makes him prone to spend money he can't afford to spend, and it makes him less powerful emotionally. The pleasure of alcohol is a bitter irony of real life and the warning here is literal.