The irony of invasion
The Hungarian people are certainly astonished when a super-powerful nation in the region decides that it would be advantageous to "annex" a new territory—and by "annexed," what is really meant is invasion. The unlikely quality of invasion makes for pandemonium as people simultaneously problem solve with basically no warning, no assurance of survival or safety, and no specific strategy for resisting Russia. The random nature of that invasion left the nation without the ability to fight back in a united way, so the efforts at rebellion are easily defeated.
The irony of departure
There is dramatic irony when the Hungarians flee their homes as refugees of war. The irony extends to all that they do not know: they do not know how long their departure will be, nor do they know whether Hungary will ever be home for them again. They do not know how they will fair abroad, or if they will even escape successfully. They do not know whether their decision is strategically correct or too extreme, but in light of the social disaster of invasion, many feel there is no other choice. If there is another choice, it is concealed by dramatic irony.
The soviet weaponry
Historically speaking, this episode was preceded by an important change in human combat. In the World Wars, Russia was noticeably behind in their technological progress, such that they often had to fight German tanks and airplanes with only horses and foot soldiers. Then, the Soviet power rose tremendously as if to say, "Never again" to being outgunned that way. Now, the ironic opposite is shown; the Russians are able to crush the Hungarians easily by using their own cutting edge military equipment against a nation without such military interests.
Budapest and doom
When Soviets overtake Budapest, the consequence is a sense of doom that is properly identified as drama from irony. The dramatic irony is that Budapest represents an important turning point between East and West in Germany. The whole of Europe becomes very interested in the happenings in Budapest, because the invasion of Hungary has seriously concerning similarities to empire-building. Only a decade earlier, the Nazis were behaving similarly in nations like Poland and Austria.
Social paranoia
When Russia sends spies into Hungary to live as normal people in Hungarian communities, that adds an element of dramatic irony to their lives, because they are unable to easily discern who is who. The social paranoia that they endure is the natural consequence of not knowing who to trust. It is also ironic in a situational way, because it means that some of the people that others trust are actually Soviet agents sent to betray them, and treachery of that kind is ironic—people don't automatically expect that their acquaintances are spies from other nations.