The irony of love lost
Although Klara is skilled at male trades and female trades, and although she passes for a man in this novel, she is a tender person with a thirst for romance. But, when WWI takes her boyfriend away from her, she is left in the ironic pit of despair, and she takes years and years of sitting alone, sewing and thinking, trying to process through it. Not only did she not get what she wanted, she had to live a nightmare worse than anything she had ever imagined.
The dramatic irony of Tilman's life
Tilman is suspected by his family to be dead, after he ran away from home and his controlling mother. This means that the second part of this book, "The Road," is dramatic irony, because when we resume Klara's story, we know everything her brother has endure, but she does not. This use of dramatic irony highlights the fact that when people were separated by WWI, they were often never heard from again, whether they lived or died, leaving the family to wonder what happened in the many, many cases that people when missing, like Tilman.
The irony of gender norms
When Tilman runs away, that leaves Klara's grandfather without a male student to take on as his apprentice. Late in his life, he realizes that no one alive in the family knows the family trade, so even though Klara is a girl, he decides to take her as an apprentice. Klara is fairly androgynous as a result, such that when she dresses in disguise as a man and works the monument job in France, no one notices. The irony is obvious—Klara was obviously able to do carpentry, because gender norms don't do what one might expect. They exist for social reasons, not because a woman or a man couldn't do the same jobs. Klara knows this from the get-go, but her family learns it too.
The irony of historical fiction
This irony is that some of the characters and events in the book are real, but we meet them through fictional characters, even the monument itself and its overseer, Walter Allward. The point of this irony is simply to point at the fact that World War I did happen. Modern estimates are that 40 million people died from WWI.
The irony of horror
In this book, Klara is alone for a very long time. Why? Well, the ending of the book suggests that, having been separated from her brother, she doesn't really have a friendship strong enough to handle the intense emotions that Eamon's death brought her. So she is locked into the nightmare of his death, without anyone to truly connect with who might help her to mourn. So ironically, she stays locked in that horrified state pretty much until her brother comes back. People misunderstand her as a loner—technically she isn't a loner, she is a desperately lonely woman who doesn't know how to talk to anyone about the fact that she is simply distraught inside.