The Five Brothers' Disguises (Situational Irony)
In their 13th year of exile, the five Pandava brothers and Draupadi decide to go in disguise in a fellow king's court. These disguises are all ironic given their real identities, providing one of the few explicitly comic episodes in this epic. Yudhisthira, for example, poses as a brahmin who is also a skilled gambler, ironic because gambling is how he lost everything and was exiled in the first place. Draupadi becomes a maidservant, ironic because she can still enjoy similar freedom to what she enjoyed as a princess, but at the exact opposite end of the social ladder. Arjuna poses a eunuch and Bhima as a cook, both meant to provide winking counterpoints to their real identities as deadly warriors, inverting their hyper-masculine identities by assuming more feminine roles.
Karna, The Secret Pandava (Dramatic Irony)
The big secret at the heart of the warfare between the Pandavas and the Kauravas is that Karna is the eldest son of Pandu, and therefore a blood relative of the Pandava brothers who he is fighting. While he is well aware of this, and repeatedly refuses to reject Duryodhana and join his brothers on account of being abandoned by his father, the other Pandavas are not. Yudhisthira is dumbstruck by grief when he learns that Karna was one of his own, for this drives home an essential fact of war that Arjuna was initially weary of: that warfare occurs between kin. While that fact is made quite literal here, imbuing the clash with a tragic irony, this could be understood as an allegorical conceit meant to illustrate that all warfare is warfare between brothers.
The Ksatriya's Dharma (Dramatic Irony)
One of the essential ironies of the epic is the dharma of the ksatriya caste, which destines them to wage terrible war, existing in direct conflict with the more generalized dharma to commit no acts of violence. Krsna's recitation of the Bhagavad Gita to Arjuna during the early part of the war is a key portion of the text, not just for explaining this conflicted dharma, but for elucidating how a person is supposed to fulfill his dharma. While perhaps still ironic, Krsna explains that Arjuna's dharma is not in conflict with anything, since every man has his own dharma and must act in accordance with his dharma and no one else's. Only by acting with detachment when fulfilling his duties can Arjuna achieve his dharma.
Duryodhana Hides in a Lake (Situational Irony)
When the Kauravas' defeat is certain, Duryodhana flees the conflict and hides in a lake to escape his own certain death. This move is deeply ironic, as it mirrors the Pandava's prior exile to the woods. Just as Duryodhana had forced those five brothers to flee into a remote part of the Earth, so does he himself. The irony illustrates how Duryodhana is getting his comeuppance in the midst of an act of cowardice.