no point in the story does Nick ever lose his true self; to that extent, he remains on the periphery of the group whose story he wants to tell. But at the same time, he becomes more deeply involved in the often sordid details of their lives and loves than he would've liked. Right until the end, Nick is unable to resolve that ironic disparity between repulsion and fascination that he feels towards the glittering world of East and West Egg.

The Great Gatsby offers many examples of irony. A number of these moments have already been pointed out in the posts above. 

The novel opens with one bit of irony that is often commented on. Nick describes himself on the opening page of the novel as someone "inclined to reserve all judgments" yet in the same paragraph he presents an evaluation (a judgment) of the many young men that have taken opportunities to tell him their stories. These stories are, according to Nick, "plagiaristic and marred by obvious suppressions." While Nick is not exactly condemning these young men and their stories, he is offering a judgment and situating himself as a narrator that will comment subjectively on his narrative.

Another example of irony in Gatsby is the scene where Daisy cries over Gatsby's shirts. 

“They’re such beautiful shirts,” she sobbed.… “It makes me sad because I’ve never seen such—such beautiful shirts before.”

This episode takes place in Chapter 5 and presents an irony within the romance of Daisy and Gatsby. The shirts are symbolic, functioning as an emblem of Gatsby's success and the material comfort that his success brings. Such success is ironic in two ways in this scene.

First, Gatsby and Daisy were once in love but did not marry because Gatsby was too poor. Acquiring wealth, he has now become Daisy's ideal match. Second, the love affair between Gatsby and Daisy is repeatedly contextualized - by Gatsby - as an affair of the heart. There is a sense that this affair represents almost a platonic ideal, a perfect romance. Yet the "heart" of the romance is as materialistic as it is emotional.

Affection and love seem to take a back seat to Daisy's impression of Gatsby's business success (and to Gatsby's desire to prove himself materially worthy of Daisy's love).

Fitzgerald originally conceived of The Great Gatsby as a satire poking fun at the pretensions of the low-class grifter Gatsby, who comes into wealth. Fitzgerald based it on the Satyricon, modeling Gatsby on a former slave in that satiric work named Trimalchio who earned great wealth and threw lavish parties. The Great Gatsby became much more than satiric, with Gatsby achieving a heroic grandeur. Yet vestiges of satire remain in Nick's verbal irony towards Gatsby.

For example, Gatsby exposes some of his endless mix of the lies and truth in his life in chapter 4. Here, talking about his days in Europe, Gatsby alludes to big game hunting in the capitals of Europe. Nick knows this can't be true, as big game does not wander free in European cities, and he almost laughs out loud. Instead, in an example of verbal irony, which is saying (or thinking) the opposite of what you mean, he imagines Gatsby chasing tigers in Paris's Bois de Boulogne. This park is a civilized spot where Gatsby would hardly chase tigers, so Nick is actually communicating that he can't imagine Gatsby chasing tigers in Paris, conveying with verbal irony that what Gatsby is saying is laughable.

An example of situational irony occurs at the end of chapter 3, when Nick dwells on Jordan being "incurably dishonest" while he is the one leading on his girlfriend in Chicago, who he views with some distaste. Who is the liar there? Nick compounds the irony when, right after thinking about how he is not being straight with the Chicago girlfriend, he mentions honesty as his cardinal virtue.

You can find lots of examples of irony in F. Scott Fitzgerald's The Great Gatsby.  Many examples show how empty, stagnant,  and self-absorbed the upper class is. Daisy's first words are

"I'm p-paralyzed with happiness."

These words convey her situation perfectly.  She would be called a one-per-center in today's jargon.  But she has nothing to do, nothing to strive for. 

"What do people plan?"

she asks.  She really doesn't know how to make plans for the future, because she has everything that she could possibly want and need now.  The irony lies in the fact that she has the happy life that so many people desire, but it paralyzes her even as it protects her from the "hot struggles of the poor."  This is precisely why she cannot leave Tom and go with Gatsby.  She would have to give up too much, and Gatsby's lifestyle would be uncertain at best.  Having it all means having too much to lose.  

Tom is another character whose words create almost humorous irony.  He claims

Nowadays people begin by sneering at family life and family institutions and next they'll throw everything overboard and have intermarriage between black and white."

This quote is quite ironic in that Tom is the one who is sneering at family life in his affair with Myrtle (and many others, as Daisy claims).  His criticism of others is more appropriately directed at himself.  And it's hard to miss the faulty cause and effect statements about infidelity leading to intermarriage. The irony lies in the fact that Tom lives the life that everyone wants, but it doesn't make him happier, kinder, or smarter.  If Tom and Daisy represent the top of American society, then we are all in trouble! 

Fitzgerald gives us many examples of irony that show the corruption of society.  George, Myrtle's husband, looks at the billboard that shows the eyes of T.J. Eckleburg and thinks he is god.  Ironically, the god he is addressing is really just a billboard.  Fitzgerald is perhaps suggesting that consumerism has become the American god.  

These are just a few examples from the novel.  I hope I have pointed you in the right direction.  

The Great Gatsby doesn't strike this reader as particularly comical, but I can think of one part where Nick's ironic commentary on Myrtle Wilson might produce some comedy.  Myrtle, Tom's mistress, is of a much lower class than either Tom or Nick.  She lives in the valley of ashes (rather than either of the "Eggs") with her mechanic husband, George.  One would, therefore, likely not expect her to behave in a snotty way -- as we might expect of Tom or Daisy.  We would more likely expect Myrtle to behave humbly, as a person who is used to less and receiving more might. 

However, once she is ensconced in her apartment with Tom and Nick, Myrtle changes her dress, and "With the influence of the dress her personality had also undergone a change."  She begins to behave with "impressive hauteur.  Her laughter, her gestures, her assertions became more violently affected moment by moment, and as she expanded the room grew smaller around her, until she seemed to be revolving on a noisy, creaking pivot through the smoky air."  Such an image, of Myrtle swelling like a balloon in an ever-shrinking room, spinning around and around noisily as she tries to impress everyone around her, is a pretty comical one, and it is ironic because her behavior is so different from what we would expect of a woman in her position.