Phenax's Influence

Subtlety and manipulation—of mind, word, and deed—are the cornerstones of Phenax's power and his influence over mortals and immortals alike. Even gods enjoy hearing what they prefer to hear instead of the truth, and Phenax is happy to give them what they want.
He takes pleasure in finding ways to subvert or corrupt champions of law, order, and justice, turning them to his cause. Whether by feeding the hubris of a champion of Heliod or subverting the moral code of a stalwart of Iroas, he tempts mortals by confronting them with seemingly inconsequential decisions, each of which offers an opportunity for the person to compromise their principles. One by one, these acts move the needle of a person's moral gauge by a small amount. Over time, these choices accumulate until the individual's fall from grace is complete.

Phenax's Goals

Phenax doesn't want to rule Nyx. He is the perennial outsider, existing only to disrupt the plans of his fellow gods. Every lie, every betrayal, delights him as it sows discord in the world. He respects a well-planned and executed grift or heist, sometimes rewarding able followers with opportunities to serve as his champions.
As the metaphorical progenitor of the Returned, Phenax also takes time to provide shelter and opportunities for his children to disrupt the mortal world.

Divine Relationships

It stands to reason that the god of secrets, deception, and betrayal isn't close with the rest of the pantheon. This is not to say that Phenax doesn't have active relationships with others in the pantheon, but his position as the patron of lies doesn't lead to close, lasting friendships.
Erebos and Athreos despise Phenax, which delights him to no end. Phenax revels in the fact that, as a lowly mortal, he was able to outwit both the Lord of the Underworld and the River Guide. Still bitter over Phenax's deception, Erebos concocts ways to torment the upstart god. Were he to discover a method to slay Phenax and return him to the Underworld, the god of the dead would pursue it over all other goals.
Phenax finds Heliod and Iroas overbearing and insufferable. Both represent ideologies diametrically opposed to Phenax's, and both have followers who regularly try to foil his schemes. In turn, Phenax does his best to upend their plans through lies and deception. After all, a fair fight isn't worth fighting.
Nowhere is Phenax's commitment to upending the status quo and angering his fellow gods more evident than in his role in the rise of Xenagos, the now destroyed god of revels. Xenagos's attacks left many of the gods disconnected from their followers, inciting a panic in Nyx. Phenax, basking in the chaos of Xenagos's plot, found myriad ways to covertly aid him until the satyr's apotheosis. Helping another mortal ascend to godhood was, to Phenax, the ultimate subversion of authority.