The universality of competition
The most pressing irony of the novel is the importance placed on competition. The universality of Everyman's name is a signal to take his universal experience of competition as a symbol indicating the true ubiquity of human competition. Look at nature—even the animals compete to reproduce, they compete for food and water, and they compete for their children. This is inherently ironic because it means that the love and attention that Everyman wants from his parents is essentially a desire to win in a mortal competition against his own brother. The situational ironic is the antithesis of love, because it is clearly each man for himself, whether brother, lover, or foe.
The meaninglessness of victory
The beta brother grows up in his brother's shadow longing for a taste of victory, assuming that the brother has experienced something important and divinely inspired in his victory in the home dynamic. That brother had more confidence because he won more attention from the parents, and then he went on and thrived in life, getting the better job and becoming wealthy. Eventually Everyman does attain victory, getting his dream girl, but he realizes that it is essentially meaningless. This is perhaps the central irony of post modern existential literature. It verges on nihilism.
Solipsism and empathy
The only difference between true nihilism and this novel is the consideration of solipsism. This man behaves solipsistically when he abandons his wife for several affairs, leaving his "dream girl" at home to take care of the kid while he gallivants around town attracting new mates. He has no empathy for her or for the child, nor for his mistresses whom he treats as dispensable and replaceable. When he gets a hot Danish model, he leaves her just the same. Eventually, though, it occurs to him that there is something mysterious about his behavior. He never stopped to consider whether they might actually be real human beings like himself. Ironically, he treats them as figments of his imagination or objects in a mindless machine-like universe.
The irony of intimacy
When he finally discovers intimacy, the experience is quite literally defined by irony. Ironically, she isn't a sexual partner at all, but an intellectual companion and a friend and colleague (something he never even attempted with all his wives and girlfriends). Ironically, she doesn't deign to make him king in her life, and he doesn't save her from her depression and ennui. Ironically, as soon as he finds someone who validates his life and helps him escape the spiral of meaninglessness, she is not saved from that spiral, but instead kills herself, leaving him behind. The meaninglessness of intimacy is painfully obvious; she still dies, so not even their intimacy is a permanent solution to life's woes.
The gravitas of death
Finally, the novel lands its plane on the issue of death. The irony of death is that the gravitas of death reorients his quest for meaning. First of all, his parents deaths are unignorable reminders that they were never gods. But, as a child, he couldn't help but accidentally assume that they were gods. He competed with his brother for their love as if it was a true reflection of God's love for them, but as it turns out, God treats all his children equally. Everyman wants redemption and passion and glory, but instead, he finds God's only universal gift. He meets the angel of death in the form of a lowly grave digger.
