I have to write an essay comparing the characters of Gatsby, Claudius and Moss as to the extent they wrestle with their conscience and how their inner conflicts amplify an important theme in the texts. Basically each character dies tragically and they are driven by their greed to attain their goals, ie. Daisy, becoming King of Denmark, and becoming instantly wealthy. Question is...how do they wrestle with their conscience, is the theme of Greed something that each character is conflicted with? Not sure how to answer this

I have to confess at the start that I'm not sure of which literary character named Moss you're referring to. If it's Sam Shepard's The Late Henry Moss, I would say there's relatively little connection between Moss on the one hand, and either Gatsby or Claudius on the other, with two exceptions. Shepard's Henry Moss is a father figure who has been elevated to a negatively mythic status by his sons. This bears some resemblance to Hamlet's hostile connection to his uncle and stepfather, Claudius, but the analogy does not go much further. It's also possible to see Moss's end, in a seedy hotel room, as a parallel to the collapse of Gatsby's world and his death.
With regard to Gatsby and Claudius, the chief similarity is that both have false or self-destructive ways of reaching their goals. Claudius has committed murder to acquire a woman and a crown. The wealth Gatsby has accumulated and the persona he has constructed for himself have as their object Daisy. As elsewhere in Fitzgerald, a central character develops an idealized view of a woman and sees a superficial world of wealth and power as an extension of her, or as a means of winning her. Both the woman and the wealth turn out to be illusions—in Gatsby, in Tender is the Night, and in short stories such as "Winter Dreams," "The Ice Palace," and "The Diamond as Big as the Ritz." In Gatsby's case, the world collapses around him partly because he has not grasped the superficiality of Daisy and of the dreamworld he has created for himself with his parties and his mansion, a kind of palace of illusion.
Claudius's world is also based on illusion, because he thinks he can get away with murder, to put it simply. Unlike Gatsby, he doesn't seem to idealize Gertrude or anything else. And unlike Gatsby, Claudius has little claim on our sympathy. It's really only in the one scene where he is shown praying that the audience and the reader feel any connection with him, and here it's because Shakespeare's language, as always, is so powerful that it awakens our emotions and makes us feel universal empathy, even for a murderer.