The irony of the anthropomorphic machine
The irony of creating beings who look like us and operate with the same logical principles we abide by—well that goes back all the way to early human mythology. The Judeo-Christian stories says that God created humankind in His own image (technically, in "their own image"), and it seems to be a basic feature of The Cyberiad that in this sci-fi world, the robots are basically humanoid and can be treated more or less like humans. That's ironic, because it goes against the obvious choice, to use robots as a symbol for mystery and unspoken power. Instead, we get a universe where the humans are like gods, and the robots are like the heroes of old.
The irony of the unknown world
Another irony like the irony just mentioned above is the irony of the unknown. This collection is packed full of humorous, Douglas-Adams-like jokes about the unknown world. For instance, in one story, the two humans are captured by space pirates, but the pirates are actually academics who just want more knowledge. This is irony on full display, that out of the vast cosmic chaos of deep space comes some PhD students with a hankering for more fun facts. It's absurd, but it's still insightful because it helps express the projection we use to make sense of the universe.
The irony of happiness
Look at "The Highest Possible Level of Development civilization." The robots tell of a utopia, a la Plato's Republic, that they concluded through scientific calculation. We actually meet this world, a strange universe with a star in the shape of a cube, so that its inhabitants are always amazed by the strangeness of reality. He meets the inhabitants of the society and finds that they're basically boring. So there is the irony of happiness on display: A perfect world would be a square world for boring, lazy, uninteresting people. In other words, happiness is shown to be overrated.
The irony of meaning
If you ask the two human heroes, these god-like engineers, "What is the meaning of life?" chances are, their answer will seem random to us. That's because the book doesn't put meaning at the center of the book. In fact, there is an inversion of the typical meaning structures: On the robot side, there is an orderly, organized hero system, where robots like Arthurian knights save princesses from dragons, as expected. On the human side, though, we see a pair of powerful beings on adventure, learning from strange situations, finding themselves in all kinds of funny scenarios.
This is a structural irony where the aspect we know almost nothing about, the sci-fi robots, go on enacting basic structures for meaning. By the way, the themes of 'meaning' and 'happiness' are treated in a number of ways, since they're the main consideration of the collection.
The irony of beauty
A common motif of humorous sci-fi is the treatment of poetry. In this collection, we see a computer that generates any kind of poetry from only a couple of words. Recall in the film iRobot, that Will Smith asks the android, "Can you paint a masterpiece?" and the android retorts, "Can you?" Well that's basically the same question here, and it also appears in Douglas Adams works. The irony is in the answer that the author gives to this question. Basically, the answer is yes, robots can create poetry.
