The irony of Agnes's book never selling
The Nice and Accurate Predictions of Agnes Nutter, a book of entirely true prophecies, was a huge publishing fail and didn't even sell a single copy. This is ironic because despite it being the only prophecy book that was completely true, it didn't sell at all. Anathema further contributes to this irony by saying to Newt, "...Agnes was the worst prophet that's ever existed. Because she was always right."
The Irony of Aziraphale and Crowley
Despite Aziraphale being the angel and Crowley being the demon, their roles are almost switched. Aziraphale is somewhat lazy, fussy, and testy, whereas Crowley, while slightly mischievous, enjoys life and humans, finding mirth in silly pranks as opposed to finding joy in absolute evil. Their attitudes should be the other way around because of their supernatural identities, and in fact, their opposing personalities are almost nonsensical because of who they are.
The irony of Pepper's name
Pepper's given name was Pippin Galadriel Moonchild, which the rest of the Them found out is a name she detests, even fighting people if they dare to make fun of it. All of the other boys have quite ordinary, boyish names, even Wensleydale who is extremely mature and vaguely effeminate. Thus, it is ironic that out of all of the children in the group, the most feisty, Pepper, has the most absurd and girlish name.
The irony of Crowley's bird argument
Upon discussing Armageddon, Crowley finds that Aziraphale has resigned himself to go through with it because he has to obey orders. He tries to tempt the angel by telling him how little entertainment and pleasure Heaven has when compared to Hell. He uses the metaphor of a bird flying to the end of the universe and back every thousand years to sharpen its beak, and how when the bird has worn down the mountain to nothing, Aziraphale 'still won't have finished watching The Sound of Music.' This is ironic because Crowley's bird metaphor is one that was originally used to describe how long the torments of Hell will go on for, but he is using it to describe the torments of the boring Heaven instead. Additionally, it is also ironic that despite Heaven being the 'good' place and Hell being 'bad', it seems that Heaven is actually quite boring and Hell isn't all that terrible.
The irony of Hastur killing the telemarketers
During a confrontation between Hastur and Crowley, Crowley escapes by going down a telephone cord and traveling through the sound waves as it rings. Hastur chases him, but ends up trapped and therefore angry, taking out his rage on a group of telemarketers by eating them alive. However, despite trying to do an evil thing, Hastur actually ends up doing a good thing because the telemarketers can't annoy anyone else with their calls.