The ironic title
One of the most obvious ironies of the book is that the title refers to contents not found in the book. This is indeed not a History at all, but rather, it is a compendium of thought experiments and stories designed to make the reader question their relationship to human history. The title is also ironic because it suggests a kind of unity among the pieces when the individual chapters are seemingly disparate or even irrelevant.
The design of the woodworm
Twice the book refers to the plight of the woodworms. The first time is when they have to sneak in Noah's Ark for survival, and the second is when they are on trial for eating the pillars of the church. Their argument is that, although building with wood is good, so is eating wood. They see God's design as one that doesn't allow tradition to just continue unchallenged. They see their own existence as evidence that it is good to deconstruct religious beliefs.
The Mountain
The irony of the story "The Mountain" is that the daughter goes to meet God to make atonement for her father, but instead, she finds herself unable to hold her convictions. Something about the uniqueness of the journey, the unique vantage of the mountain, and the unique solitude of the monastery make her consider transcendence. The story suggests that religion might be more nuanced and mysterious than meets the eye.
The rejection of refugees
The story places Jonah's story in tandem with two other stories: one where the survivors are helped and cherished, and one where the survivors are despised. This is designed to illustrate the absurd irony of denying help to refugees, like the Jewish refugees mentioned who in 1939 were denied access to America and other countries because of hatred and racism. The Titanic is opulent and regal, and those survivors are helped, but the needy refugees are abandoned.
The final chapter
The final chapter, "The Dream," is a full-blown religious epiphany offered to the reader for consideration. This depiction is similar in form to the apocalyptic visions of the Bible and their descriptions of the New Heavens and the New Earth that will come after the end of the world. Although this is an ironic way to end the book, it does make sense, because those apocalyptic prophecies are part of the Noah's Ark story, so to speak. In any case, the absurdism and existentialism of this book make it seem unlikely that it should end the way it does.