Explanation of irony: https://literarydevices.net/irony/ Stroke of irony - An event occurs which creates an ironic moment. Example: Last week, my neighbor was giving me unwanted advice about raising children. He claimed his children were perfectly behaved. Then, we heard screams. In a fit of rage, his older son was pummeling the much smaller younger son. What a stroke of irony! His own children put the lie to his words.

Further to what Simon has written, the phrase implies something unexpected, that perhaps was not supposed to happen, but that changed the expected outcome.

Think of a clock with a bell striking the time. At the stroke of midnight - something happened. So it is a more interesting way of saying they used irony to make some point.

HI Mona, basically is like "sense of irony" or "ironically"