How can I discuss the following statement in regards to the main characters of The Great Gatsby:
"Most characters in the Great Gatsby are involved in deception, self-deception and delusion, depending on their perception of what constitutes reality."
To treat this statement about The Great Gatsby, simply take one character at a time and see if he/she suffers from illusions or practices deception. I'm not sure I would worry too much, especially while your gathering evidence, about the "perception of what constitutes reality" part. That should come clear later, after you've gathered evidence, but even if it doesn't, figuring the illusions of and deception by the characters is most of what you're looking for.
For instance, Gatsby suffers from the illusion that Daisy loves him as much as and in the same way that he loves her. She doesn't. This is a beautiful illusion, but it is still an illusion. Gatsby dedicates five hears of his life trying to recapture a past, that in reality, never existed in the first place. He suffers from illusion and self-deception. He tells Nick that, of course, one can capture the past. But, of course, one cannot, especially when that past never even existed. Gatsby's relationship with Daisy from the past is Gatsby's reality. But it's a faulty reality.
Nick is another example: he deceives the reader, beginning his story with an anecdote (his father teaching him) that demonstrates the fact that he doesn't judge people. But he does judge people. This is deception. Reality to Nick is his honest character, and his objective nature. But these, too, are illusions.
Tom and Daisy also have illusions and practice deceptions. I'll leave those two to you.
Gatsby is involved in deception. He is not who he appears to be. He came from a poor family and he worked his way to wealth through what we can assume were some business deals of the bootleg or black market variety (as evidenced by his connection with Meyer Wolfsheim). He portrays himself as an Oxford man, and he did attend Oxford for a term, but only because he was allowed to after his time in the service. He does not come from the background that he makes himself appear to come from. In fact, he has put on this mask as a means of getting Daisy whose philosophy is that rich girls don't marry poor boys.
Daisy practices self-deception. She decieves herself into oretending to be happy in a marriage to a man who cheats on her. She believes in the fairy take romance that she starts with Gatsby. Ultimately, she decieves herself and those around her when she retreats to her "happy family" even after killing Myrtle, a crime for which she is never punished.
Tom deceives himself in his belief that Daisy is unaware of his affair.
Myrtle deceives herself into believing Tom loves her and into believing that she is a part of his world on their jaunts to the apartment in the city. She deceives herself into thinking that he will take her away from her poor existence at the gas station.
Nick's self deception is far less evident. He has a general belief in the goodness of humanity that is out to the test by the people he meets. His friendship with Gatsby teaches him the importance of friendship, but it also exposes to him the fact that money and power are not really all that they might have appeared to have been to him in the past.
A final interesting character to consider is Meyer Wolfsheim. He deceives people daily - it is his "career" in a sense. But, he is also perhaps the most grounded and more of a realist about life. He knows that what he does is dangerous, but he takes care to steer clear of the fallout. He knows that people die, people are killed, and he values them for who they are while they are alive and does not mourn them overly much when they are gone.