Nick is definitely an outsider. This is important to the reader so that we can see the different personalities and traits of the West Egg people, the East Egg people, and even the Valley of Ashes people. Not only is his cottage not a mansion, nor is it slovenly, it just doesn't fit in anywhere. His way of thinking is so very different from all of them. The character who thinks most in line with Nick would be Jay Gatsby. Jay doesn't use people. In fact, he lets them use him. All he wants is for Daisy to show up one night so that he can see her again and win her back.
People like Daisy and Tom use others and then throw them away when they're done with them. We wouldn't see it quite that way if Nick wasn't the narrator. As for the party, Nick never goes until he gets an invitation. All the other people who flock to his house and drink and eat his drinks and food appear without invitations. Finally, Jay sends a messenger over with an official invitation. So Nick does eventually go, but he went about "participating" in the correct and proper way.
Nick Carraway's status as an outsider is established from the very beginning of the story. Nick comes from the Midwest, for example, and does not belong to the same social and economic class as the other characters. He is not rich like the Buchanans, for instance, nor well-known in his occupational field, like Jordan Baker. Moreover, unlike his rich neighbors, Nick does not live in a large, palatial mansion. In fact, Nick describes his house as an "eyesore."
Nick does not behave like the other characters, either. He waits to be invited to one of Gatsby's parties, for instance. When he finally arrives at Gatsby's house, he wants to meet Gatsby and learn about him first-hand, not simply gossip and speculate about his origins. Nick also prides himself on being honest, a trait which is lacking in characters like Jordan, who cheats at golf, and Tom, who cheats on his wife.
When Gatsby dies, Nick's status as an outsider is further reinforced. He is the only one of the main characters who seems to genuinely mourn Gatsby's death and who attends the funeral. This helps him to realize that the people around him are shallow and self-centered, prompting him to leave New York and never return.