The irony of ugliness.
This should be obvious, but it's worth noting: The name of the book refers NOT to the demeaning and racist views of the majority, but to a particular person who was literally ugly. The irony is that his visual ugliness was no obstacle in his success, but the emotional and ethical ugliness of the majority might have caused the terror of the Vietnam War.
The irony of white superiority.
White people who think they are superior are a highly ironic group of people, because by their own religious views, "The first will be last, and the last will be first." The entire principle of civilized American society is that we adhere to religious views from Christianity, and that is absolutely not reflected in the attitude of white superiority, and this book does a good job of bringing attention to that hypocrisy. All humans are equal, regardless of race or religion.
The irony of the Vietnamese War.
The great irony of the Vietnamese War is the reversal of fate. It is the only war that the US military ever lost, and they did lose, regardless of what kind of what they wanted American citizens to believe in the 70's. The Americans were destroyed in that conflict, and the Vietnamese people cited the arrogance and superiority complex of the west in their reasoning. This book is a depiction of that irony, but it doesn't exactly make the connection to the Vietnamese war, instead veiling the criticism through the fictional country of Sarkhan.
The irony of humility.
As previously noted, the thrust of the novel concerns the good example of the ugly American. The irony of humility is evident here, and also in the fact that such a depiction caused the Kennedy Administration to adopt an "Ugly American" approach in starting the Peace Corp. Literally, the legacy of one humble man transformed American foreign policy forever. Therefore meekness is ironically powerful.
The irony of humanism.
The irony of humanism is that it doesn't matter what kind of human you're talking to—if they're human, they should be treated as essentially equal. The fact that this is ironic is a grave tragedy, because it should be self evident, and ironically, those were the principles that America was founded on.