The irony of trauma
When the police came to arrest her family for being Jewish, that was a traumatic moment for the entire family, and when they discovered their new fate as prisoners in a ghetto, that was traumatic, but none were as traumatic as the death camp. In fact, we can see from this that there is an essential connection between irony and trauma—Heda is traumatized because her reality is so far from what she considered possible that her entire world view shatters under the unimaginable weight of the Holocaust.
The irony of disorder
Heda remarries after she is freed from the death camp. She marries a man with liberal ideas who is kind of a utopian lad, meaning that he believes that if humans continue to work together, they could evolve their form of government to something more universally beneficial. Ironically, he spoke too soon, it seems, because in the frantic aftermath of WWII, he is killed for his Communist sympathies. This is ironic, because it is clear that he was only passionate about civic balance and order, but those opinions were not tolerated.
The irony of moving
Heda is old when she moves, which is ironic. Moving tends to be more of a young woman's game, it seems, but Heda notices this and observes the irony, defending herself by saying that actually, it's important for her to have some final years of peace and unwinding after such a traumatic and horrifying life. She believes America will provide her with a new normal, and from there, she expects to heal her point of view, but ironically, she must uproot herself again, like a fox without a den.
The irony of life and struggle
For Heda, her entire life has been a struggle. When she and her husband decide to lean left politically, it is because of their suffering. That means that ironically, they suffer more than others because they are constantly aware of their suffering. This is literally true when Rudolf is killed for serving his civic duty. It seems that those who don't have to struggle in life are given way easier fates than those who suffer. In other words, suffering seems to be unfair.
The irony of survival
For the dead, life is over, but for Heda, she continues on with the memories of her heartache and loss and trauma, but there is an inherent irony in her survival. Not only is she a survivor, but she is always a survivor, because her fate is so difficult that she has to white knuckle her way through entire years of mourning and paranoia. Imagine if two times in a row, your family was taken from you by the police. That's essentially what she was made to endure, but ironically, her testimony is encouraging, because she struggled and persevered.