Christ.  One level ofirony is the difference between what Christ valued versus what "Jay Gatsby" valued.  For Christ, humanity ought to love one another, to exhibit peace, love, and understanding.  Most importantly, the Bible repeatedly depicts Christ frowning upon wealth such as when he states, "It is easier for a camel to pass through the eye of a needle than for someone who is rich to enter the kingdom of God" (Mark 10:25).  Gatsby, for all intents and purposes, is the exact opposite of this.  As the passage above states, Gatsby was about "the service of vast, vulgar, and meretricious beauty." Both Gatsby and Christ are about their "Father's business"; however, their father's respective businesses are very different.  For Christ, his father is God, whose Golden rule is to treat others as we would want to be treated.  For Gatsby, his father is Dan Cody (the wealthy copper mogul who Gatsby fashions himself after).  Christ spends his adult life looking after and healing people who require us to look inward when we see them (i.e. lepers, the seriously ill, prostitutes).  Gatsby spends his adult life tending after a façade (i.e. a beautiful house with nothing in it, friends who aren't friends, a library with books that have never been read, a woman married to another man and who is likely hollow inside).

The above explanation is the main level of irony present in the passage.  One could, however, make the argument (though it is likely not what the question posed is getting at) that there is another level of irony in the fact that Gatsby is self-fashioned.  The phrase "Platonic conception" refers to Plato's theory of knowledge that we first conceive of an ideal (what he calls a "form") and once we conceive of the ideal, we can realize it or see it in reality (or, what his student Aristotle might refer to as "particulars").  In this case, Gatz conceived of "Jay Gatsby" and then made it happen.  Gatsby is a persona, a conception, or an illusion.  Christ, on the other hand, was anything but a façade.  He worked in an opposite fashion by seeing the world as it was and then going inward to find salvation.

If the comparison were extended in the novel, the obvious comparison would be Gatsby's death.  Christ, of course, dies for the original sin of humanity.  His sacrifice provided salvation for all humanity.  Gatsby, however, died for Daisy's sin of running over Myrtle.  Both could be said that they died for something they believed in and both can be said that they died for a people who was not worth saving.  The irony dissipates in this extended analogy, and drives home the rather depressing and caustic worldview of Modernist writers like Fitzgerald.  That is, to think that, in Fitzgerald's mind, we are all nothing but a bunch of Daisy and Tom Buchanan, and that the best modernity can do for the ideologues growing up is to offer them the role of Jay Gatsby.

In the quote you included, Nick is trying to understand the reason James Gatz, raised in a farming family in North Dakota, became Jay Gatsby. Verbal irony can be presented as words, actions, or narratives that indicate the opposite of what the set of words generally mean. Jesus preaches and the bible encourages a completely different lifestyle to that of Gatsby. Jesus lived a modest life as a preacher, while Gatsby surrounds himself with opulence. Nick makes this biblical allusion to describe him, when in reality, the millionaire's lavish parties and immense wealth demonstrates the exact opposite.

Situational irony occurs when readers possess more information than a character and are aware of a different meaning to their words. Nick is referring to how Gatsby reinvented himself, just as Christ was reborn after his crucifixion. Nick is unaware that his words also carry additional meaning. Nick is unaware that Gatsby will be killed by the end, making his words predictive of Gatsby's demise.

Please refer to the following eNotes thread, as it discusses this association as well:

Verbal irony occurs when a statement means the opposite of what is said.

In this paragraph, Nick is attempting to get inside of Gatsby's past, seventeen-year-old mind and understand what he was thinking when he orchestrated his rebirth from James Gatz, son of shiftless farm people, to the more glamorous Jay Gatsby. The idea of rebirth makes Nick think of divinity.

The statement is ironic because the "god" Gatsby sprang from, as far as Nick is concerned, is Gatsby's own "platonic [ideal]" concept of himself. He makes a god of a certain self-concept: his "father's business," which is really his own adolescent business, is the pursuit of "vulgar" beauty and wealth. This is how a teenager might think, and Nick ends by asserting that because he never changed worshiping this concept of himself as an ostentatiously wealthy and glamorous figure, Gatsby was forever an adolescent in arrested development.

Comparing Gatsby with Christ is ironic for several reasons. Here are three.First, Christ's father always knew what Jesus was doing. Gatsby's father does not know his business. Second, Jesus was selfless. Gatsby lacks a self: he is recreating himself, trying to fill a tremendous and painful gap or hole. Third, Jesus brought a mission and a message to others; he had followers. Gatsby had people who took advantage of him, but his influence evaporated once he was dead. Jesus was more influential after death; Gatsby's influence dies with him.  

The quotation that calls Gatsby a "son of God" is ironic on several levels.

To begin with, although Gatsby is "a son of God" and removed from the merely human realm in the sense that he has dedicated himself to something outside himself, an ideal, the ideal is not very exalted. As the quotation goes on to say, he has put himself in the service, not of humanity as a whole, but "a vast, vulgar, and meretricious beauty."

The second and more profound level of irony is in the way the quotation foreshadows Gatsby's end. He will soon be killed by George, Myrtle's husband, who has been told by Tom that Gatsby was driving the car that killed Myrtle. In other words, Gatsby will die in the service of his ideal as a result of an unjust judgment, ironically evoking the sacrifice of Jesus on the cross. A martyr to his mundane ideals, Gatsby ends up assuming the responsibility and paying the price for the sin of someone else, Daisy.