Physical power
The Spartans are an elite combat force. Their physical power is unparalleled, and whereas Athenian soldiers receive some training, their training cannot compete with the training that Spartans give to their soldiers. Spartans are trained from youth. And yet, that physical power leaves them continually over-confident and under-prepared. One clever decision can render their advantage completely irrelevant, so the battle is a game of wits.
The empty invasions
The most tangible irony in the History (maybe in the entirety of Greek history) is when the Spartans charge into town after town to take it over, only to discover that there isn't anyone there. They can have the city if they want it, but it defeats the point. Knowing that Sparta would probably run a campaign through the towns, Pericles evacuates the towns preemptively, making Sparta feel pretty silly. It is not encouraging to know your enemy is steps ahead of you.
Disease and irony
That doesn't mean that the Athenians have an easy war on their hands. Their use of strategy is enough to combat Sparta's excellent training and physical prowess, but when a plague sweeps through the Athenian ranks leading to the death of their general and many, many soldiers, that is beyond their control. Fate is ironic to them, because they had the situation under control, for the most part, but no one is in control of a war, it seems, because circumstance can play such a strong role.
The ironic treaties
The treaties that conclude the war are ironic because they aren't real treaties in the truest sense of the word. They offer a few years to either side to rebuild the damage that years of battle have done, but each side is still paranoid about the other side invading them, so eventually Athens invades Sparta, but surely Sparta didn't want to end the war. They wanted to keep fighting until they overthrew Athens, but without resources, they offered peace treaties. The war continues after the History about it ends.
The timelessness of war
Although the war happened a long, long time ago, the History of the Peloponnesian War is relevant to modern day geopolitics, which is ironic. This means that human nature doesn't change as much as some believe. Although weapons evolve through technological growth, the progress doesn't change basic human psychology. The Athenian use of strategy is still laudable, and the dangers of over-extension or rashness is still applicable today.
