Arbiter is Greg's best friend. The first time they met, in The Spider, Arbiter was afraid of Greg (since he's an arachnophobe). Later in the episode, he stood up for himself and insulted Greg and told him to get lost. It really hurt Greg's feelings. He wrote on a sticky pad that he just wanted to hang. Arbiter then felt bad so he decides to overcome his fear and let Greg stay. Arbiter and Greg really got along. They play scrabble from time to time. But when Arbiter was too interested in Trent and Claire's wedding, they started hanging less. Greg usually looks after Arbiter, because he gets upset and starts drinking. Greg tells him to go easy on the booze. Later on, Arbiter was talking to Claire about Greg. He says that Greg's really cool, but he can't get over his appearance. In the Cheaters episode, Greg tells Arbiter that he heard what him and Claire said about him. He decides to run away, but comes back and saves Arbiter and Chief from Trent and his friends.
Master Chief hates Greg, mostly because of his appearance, and Greg doesn't like Chief all that much either. In The Spider episode, he attacks Chief for double-crossing Arbiter. He also ties Chief up with some silk after Chief threatened to kill him. Chief eventually calmed down and just let Greg be. Throughout the earlier parts of Season 5, Greg sometimes argues with Chief, but only stating hateful facts about him, not really insulting him intentionally. In the episode Cheaters, he ties up Chief in the bathroom, in favor of Arbiter. He apologizes to Chief however. This shows that Greg might show a little respect for Chief. After he was free, Chief wanted to invite Greg for a game of Reach. Greg was pretty happy, and wanted to join him. But unaware that Chief actually wanted to kill him using his "roflknife". Even after that event, Greg still shows a bit of respect for Chief. This shows Greg is loyal to even his roomates.
Upon Greg's return in "The Reunion," we begin to see more of Greg's view on Chief's behavior with a variety of angry faces such as '>:(' whenever Chief enters the same room as him. Like Arbiter and Cortana, he too sees Chief as an annoyance and does not appreciate Chief's mean-spirited attitude.
In 'Heat', Greg surprisingly helps Chief by lying to Arbiter and covering up Cortana's death. He was unwilling to do so at first until Chief pointed out that it would only make living in the apartment even worser than it already is perhaps showing that Greg dislikes living there and that he is miserable too or that he didn't want to make Arbiter upset & worse than he already is.
Claire and Greg never spoke to each other. Claire is aware of Greg and curious about him, but she hates spiders. Greg is saddened because of her hate for spiders.
Greg and Trent never spoke throughout the entire series. In Collapse, Greg fragged Trent's whole staff, but this was to save his friends rather than out of hatred of Trent.
Greg and Cortana get along well. Greg brought Cortana to Jon's new apartment after she was stuck at Jon's old one for a long time. Cortana is not repulsed at all by Greg's appearance and actually asks whether he is a real spider or a toy spider at one point.