Otherwise known as "Black Peter," this ex-captain of a whaling ship (we dislike him already) is murdered by getting a harpoon shoved through his chest. Given what we learn about Peter during the story, though, we find that he wasn't an entirely innocent victim. First off, he was a drunk and was an abusive husband and father. We also find out that he murdered an investment banker guy in order to steal his super secret stock tips years ago. Peter's crew wasn't all that moral either, and his former first mate ends up murdering him during a fight. The other notable thing about Peter is that he doesn't live in his nice house; instead he lives in a little shack that he built. The inside of said shack is decorated to look like the inside of a ship's cabin. Clearly, this man missed the sea, and he probably shouldn't have retired to live off all his stolen money.
Captain Basil is actually one of Holmes's aliases. As Watson explains, Holmes has a number of false identities and secret hideouts throughout London. Holmes enjoys performing, disguises, and dressing-up, so it's no surprise that he decides to occasionally moonlight as a ship captain. This identity is crucial to solving the case as well. He uses this identity to lure the killer to Baker Street, where Holmes then uses his detective-mojo to get a confession.
Neligan appears to be the murderer of Peter Carey for much of the story, which of course means that he isn't. Neligan is actually just a young man trying to restore his father's good name. His dad was a banker who screwed over a lot of creditors after he disappeared. Neligan insists that his dad didn't run off with all the money. He managed to trace some of the money back to Peter Carey, and he came to confront him. But he found Peter dead. Then John rather foolishly returned to the scene of the crime in order to pick up a book he'd dropped. It seems like he's the killer, but Holmes notes that John couldn't have harpooned someone to death, as he is a puny. This small detail leads Holmes to the real killer, who explains how Peter actually murdered John's father.
Patrick was Peter Carey's first mate on the Sea Unicorn. Yes, the tough and mean Black Peter, killer of whales and men, stealer of stock tips and money, was the captain of a ship called the Sea Unicorn. Patrick killed Peter in self-defense (apparently he defends himself with harpoons) during an argument. The two were arguing after Patrick came to confront Peter in his cabin. Patrick wanted in on Peter's financial scheme. Despite his shady actions, Patrick comes across as a somewhat stand-up guy, if only because he's so forthright with Holmes.
These two women are very downtrodden and aren't all that upset by the death of the abusive Peter Carey. Watson is made uncomfortable by them and describes how he is relieved to escape the oppressive and sad house in which they live.
These are the two men who answer the false ad placed by "Captain Basil" in order to lure Peter's killer to Baker Street. These guys were dismissed since they clearly weren't strong enough to harpoon anyone to death, but Holmes did pay them for their trouble.