How does irony add meaning to the overall story of The Great Gatsby?

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.