The Irony of Chester's Mission
In school, Chester was punished for speaking Navajo. He grows up feeling continually ashamed of his native heritage, but when he gets to the war it's his saving grace. The same government which forced him to learn English is now begging him to use his Navajo for their benefit.
The Irony of a Native American Serving in the U.S. Military
After centuries of injustices toward his people, Chester still volunteers to enlist in the military at the outset of the war. He recognizes that he must set aside his feelings in order to protect his family. America is still just as much his home as the U.S. citizens whom he serves beside. Consequently he puts on the uniform of his oppressors.
The Irony of The Unbreakable Code
The code which the code-talkers write is really just a variation of their native language. If the Japanese had any knowledge of American indigenous peoples they may have been able to crack the code. It was simply too foreign for them to have any idea that it was Navajo they were speaking.
The Irony of Chester's Divorce
Ethel and Chester never had a very happy marriage. Rather quickly after marrying they realized that they were not all that compatible and neither was willing to put the effort into the marriage in order to make it successful. Years of disfunction went by. This is why the divorce was just a formality; they never really intended to be successful together.
The Irony of Dora's Death
Dora invites Chester to live with her after Stanley dies. She tries to help him through his grieving process. As unfortunate as it is, she dies just when he's starting to recover. Now he must work through his grief over losing her elsewhere.