You may get different answers but in general the biggest irony is how, despite the self-discipline, strength and courage of the soldier, it is not he who takes control of the war. In fact, it is the War takes control of the soldier, and of itself.
This is illustrated with the major. He is the anchor of the story, and the man who everyone looks up to for his bravery, strength and courage. His character exemplifies the irony of War: He has lost control of all he had.
He refuses to believe that a machine can fix his hand, he refuses to cry over his wife's sudden death, and he refuses to accept any advice from the narrator, or the other soldiers. And yet, he exemplifies how War takes control, and not the soldiers.
The narrator of Hemingway's "In Another Country" is a wounded American soldier rehabilitating in Milan during World War I. While never named, the soldier is most probably Nick Adams, who was a consistent character in many of Hemingway's short stories. There are three good examples of situational irony and one example of verbal irony in the story. Situational irony occurs when an event or situation contradicts the expectations of the reader. Verbal irony occurs when words are used to suggest the opposite of what is meant.
The narrator often goes out to a cafe called the Cova with three other wounded Italian soldiers. Two of the men have the same medals as the narrator but it is revealed later that the medals were awarded to the narrator simply because he was American and after that they treated him differently because, presumably, they had seen significant combat action while the narrator had been wounded by "accident":
I was a friend, but I was never really one of them after they had read the citations, because it had been different and they had done very different things to get their medals.
It is ironic that the narrator should receive the same medals for doing much less in the war than the two Italian soldiers. Another ironic situation involves the boy who wore the "black silk handkerchief" who had specifically trained to be a career soldier and had gone from a military academy to the front line and had been wounded within an hour after arriving.
Verbal irony involves the Major who often talks to the narrator while they are working on the rehabilitation "machines." When the narrator tells the Major he hopes to be married one day, the Major angrily replies, "The more of a fool you are...A man must not marry." It is ironic because the Major himself had recently been married upon his return from the war. He had been quite happily married until his wife suddenly died of pneumonia. Also ironic is the fact that the Major survived the atrocities of war, yet his young wife died after being "sick only a few days."