Irony of the Good-Luck Piece
On a whim, Chrono picks up a piece of shattered, twisted metal debris from the Martian war effort and keeps it, calling it his "good-luck piece." This seemingly insignificant piece of metal, however, is actually the most important thing in human history: it is the component of Salo's spaceship that the Tralfamadorians have been guiding humanity to manufacture for millennia, the sole purpose for humanity's existence. Unbeknownst to Chrono, his randomly selected souvenir is the result of thousands of years of alien manipulation, not simply a piece of scrap metal.
Irony of Constant's Religious Persona
In his absence, Malachi Constant becomes the primary figure in Winston Niles Rumfoord's new religion, the Church of God the Utterly Indifferent. Being effectively heralded as the most important person in human history, it might seem that he would be welcomed back to earth. On the contrary, however; when he arrives home, he is shunned as no longer necessary, being banished to the distant moon Titan to allow his name to regain its former legend.
Irony of Unk
At the beginning of the novel, Malachi Constant is a young, relatively intelligent man with a lot of money and a large capacity for debauchery. When his fortunes take a turn for the worse, however, he is randomly recruited for the Martian army, becoming a thoughtless brute named Unk with no capacity for critical reasoning at all. This transformation is particularly ironic because by transforming into Unk, Constant loses everything he prides himself on: his decisiveness, his possessions, his mind, and women.
Irony of Human History
The book's ultimate ironic revelation occurs in the last chapters, where Salo reveals to Constant that the entire development of human history was controlled from afar by the Tralfamadorians via mind control, in order to manufacture a replacement part for Salo's ship, as the Tralfamadorians couldn't be bothered to bring it themselves. All of humanity's greatest achievements - the Great Wall of China, the Kremlin, etc. - were actually shaped by the Tralfamadorians as messages for Salo, who was watching from the moon, saying unremarkable things like "We are doing the best we can." This is the greatest irony of the book: all of human history is so inane as to be essentially meaningless.
Irony of Constant's Death
By the end of the book, Constant has endured all sorts of crazy adventures, traveling from Earth to Mars to Mercury to Earth to Titan, being brainwashed and deserting the Martian army and being bred with Rumfoord's wife, among many other insane events. It's been miraculous that Constant has survived this long. Once Salo repairs his ship, however, he drops Constant back on Earth before departing, and Constant simply dies of exposure on a bench in Indianapolis waiting for a bus. This is an ironic end for someone who has survived so much, and it is the ultimate anticlimax for a random, irony-filled book.
