The Irony of Prayer
Inanna is herself a goddess, but she is not ultimately powerful. In order to protect herself in her sister's kingdom, she instructs her servant to pray to other gods for her. Enki honors Inanna's request because she has demonstrated the humility to accept help. She could have perhaps insisted that she will survive the affair, but instead Inanna chose to present herself as a servant to Enki, in need of his grace.
The Irony of Dumuzid's Unfaithfulness
After passing up three faithful servants as sacrifices to her sister in her stead, Inanna reunites with her husband, Dumuzid. His depiction is ironic because he is the only one to not have mourned her death, but he is her husband and thus most naturally expected to mourn her passing.
The Irony of Inanna's Power
Ereshkigal orders Inanna to be stripped naked and bare before her for fear of her sister's power, but when Inanna does arrive naked she still possesses more authority than her sister. Inanna sits on Ereshkigal's throne without complaint from the throne's rightful owner. Her beauty has only become more evident in her nudity, despite her sister's intentions.
The Irony of Ereshkigal's Anger
Ereshkigal is offended that Inanna is determined to enter her kingdom because it is forbidden, but Inanna only approaches in order to honor Ereshkigal's husband's death. She has come to mourn with her sister, but Ereshkigal chooses anger instead of gratitude and love. She allows pride over decorum more importance than her sister's motivations.
The Irony of Enki's Demons
Enki creates life to spare life. In order to rescue Inanna from her untimely death, he creates entirely new beings to descend into the Underworld after her, yet these demons still cannot pay her ransom. Inanna must sacrifice a living being from above to serve her sentence in the Underworld. Although Enki's creations are living, they are now supplemental lives who cannot pay the sacrifice because of their addition.