The man's actions reveal clue of his character. He is abusive, even to the point of murder. He describes a series of actions that mark his descent into evil. The way he writes and thinks are difficult enough, but the things he claims to have done (i.e., murder his wife and his cat) characterize him as a murderer, who happens to be an abusive and cowardly person. The man's actions also characterize the other characters as victims.
The man's wife is characterized, until the end, by her seeming lack of action. She is described as dangerously passive. At the end of the story, this changes. She actively thwarts the murder of the second cat. In fact, she dies defending him. This characterizes her as a courageous hero.
Since the man and his wife aren't described, this one applies only to Pluto and the second cat. The fact that both cats are missing an eye makes them hugely sympathetic characters. Even if readers aren't fond of cats, they will likely feel sorry for cats with missing eyes.
This one is fairly obvious. All the main characters share a very unhappy home life. But it shapes their characters differently. It characterizes the narrator as a victimizer, and the wife and pets as victims.
In Roman mythology, Pluto is the god of the underworld, a kind of king of the dead. But, this doesn't really help us characterize him, because, after all, it was the man who named him. Maybe this tells us more about the man than the cat. Why might he have named his cat Pluto? Is it possible that the narrator intended to prepare readers to think of the second cat as some kind of supernatural monster? If not, does his choice of names suggest that even before he started drinking, he had a fascination with deathly and ghastly themes?
(By the way, the dwarf planet Pluto wasn't discover until the 1930s, so Poe wouldn't have known about it.)