Are all three types of irony used in "By the Waters of Babylon"? Please give examples if they are.

Dramatic irony is when the audience knows something that characters in the story do not. We as readers know that John, the narrator, is describing New York City, and we know that in his visions he sees subways, airplanes, and nuclear war. John, coming from a far less technologically advanced culture, cannot understand as we do what he is seeing, and must describe it terms of his own context.
Situational irony arises when a situation is the opposite of what it seems. John and his people think gods built the big cities that are now called Dead Places, but we, as part of the civilization he is describing, know they were built by anything but gods. John will come to understand at the end that men built the cities, but he will not understand the full irony of the fact that the so-called "gods" destroyed themselves with nuclear weapons. Rather than be worshipped, our people should serve as a warning.
There is not much verbal irony in the story as John takes everything he sees with great seriousness and reverence, but there is some irony in George Washington's name being reduced to the letters ASHING, when his levelheadedness might have prevented a nuclear war and the ashes it produced.

There is definitely dramatic irony in "By the Waters of Babylon." Dramatic irony is a device that authors use to create situations where audiences know more about a situation than the characters do. 
In "By the Waters of Babylon," this kind of irony begins appearing once John arrives in the Place of the Gods.  We read about "god-roads," "SUBTREAS," and "ASHING." Those details allow readers to begin realizing that John is wandering around a fallen, post-apocalyptic city. Details continue to emerge about cold and hot water piping and the Grand Central Terminal. John is incredibly naive about what he is seeing, but readers eventually realize John is in is New York City. We are able to deduce that some kind of nuclear holocaust destroyed the human population, but John is completely unaware of all of this until the very end of the story. After he has his vision, then John realizes the gods were really regular people.