Sir Eustace is our murder victim in this story. He is a wealthy guy, but we come to learn that he was also abusive to his wife. For much of the story we think that a gang of thieves murdered Eustace during a home invasion gone awry. But Holmes eventually uncovers the real killer, Lady Brackenstall's boyfriend. Holmes and Watson feel that homicide was justifiable in this case, since it was in self-defense and since Sir Eustace was such an awful man. Holmes and Watson cover things up accordingly and the police continue to think that a gang of thieves killed Sir Eustace.
Mary is the long-suffering wife of Sir Eustace. Originally from southern Australia, which was part of the British Empire in this era, Mary finds English life stuffy. In this time period, far-off places in the British Empire (Australia, South Africa, India, etc.) were a lot like the old western frontier in America. Things were a lot rougher out there and strict social codes were relaxed. So Mary has trouble adapting from her freer life in Australia to her new life as an English aristocrat. Mary also stands out in these stories for not confessing everything to Holmes. She actually never tells him the truth directly; Holmes has to hear it from her secret boyfriend, Jack Crocker, instead.
Jack Crocker was an officer aboard the ship that brought Mary Frasier to England. He fell in love with her then, but respected the fact that she was marrying Sir Eustace at the time. However, when he found out that Sir Eustace was abusing her he became more involved in her life. Mary eventually fell in love with him as well, and Jack ended up killing Sir Eustace in self-defense during a confrontation. Jack also wanted to stop him from further harming Mary. In a notable scene, Holmes and Watson play judge and jury to Jack after he confesses. The two men find Jack "not guilty," and Holmes tells him to disappear for awhile before coming back to court and marry Mary Frasier.
Theresa is Mary Frasier's loyal maid who has been with her for years. Theresa is actually the mastermind of the cover-up of Sir Eustace's murder, and she remains coolly composed for much of the story. Her only notable outburst comes after Holmes accuses Mary of lying; Theresa throws Holmes out and scolds him for speaking that way to Mary. Theresa is very protective of Mary and in many ways acts more like her mother than her maid.
This famous gang of criminals is the one that Mary and Theresa blame for the death of Sir Eustace. Unfortunately for them, the Randall gang was arrested in America soon after this. So unless they could teleport, they didn't commit the crime. However, the detectives on the case think that there must be a group of Randall gang copycats running around, and the case is eventually dropped.