Please note that some of the backstory information has simply been strongly suggested by the strips while other parts have been stated directly.
Cutter John. Originally a Vietnam vet shot down over Saigon who lost his legs and gets around in a wheelchair. In the updated strips he's now an Iraq War vet who suffered the same fate. The general idea is that the Meadow, where all of the characters live, is where he goes to reflect. The strong implication is that the characters in the Meadow exist solely in his mind and are his way of distracting himself from his existence by inventing a host of imaginary friends. His favorite activity is to roll in his wheelchair down a steep hill in the Meadow with his friends on board pretending he's the captain of the Starship Enterprise (very rarely other popular spaceships.) He realy likes women and will go to all sorts of methods to court them and they tend to like him, but the relationships never last because his friends in the Meadow are far more important to him.
Milo Bloom. As his name would suggest Milo's family owns the Meadow and the Rooming House where most of the characters live. He runs the local newspaper and tries to be as strict a rationalist as possible. He exists as narrator telling the people of the Meadow what is going on. Because he believes in being objective he never stops things from happening even when he knows they are Very Bad Ideas.
Binkley. A young boy who symbolizes the extreme left wing of American politics. He will take every fashionable liberal cause and then take it to extreme conclusions. (After going vegan for a bit, for example, he realizes that he's eating germs every time he breathes and that fills him will guilt.) In his bedroom is the Anxiety Closet. This is filled with all sorts of monsters, ranging from the boogeyman to a Dick Cheny presidency. He is also obsessed with pop culture.
Hodgepodge and Portnoy. While technically two distinct characters they are almost only ever shown together and always agree with each other. The are the anti-Binkly. They will take every fashionable conservative cause and take it to extreme conclustions. The one exception to this rule is that at one point Hodgepodge gets talked into joining the Glam Metal Band DeathTongue. Portnoy wants nothing to do with that.
Binkley's Dad. A stressed out single dad who cannot figure out his son at all but does his best. He exists mostly in reaction to Binkley.
Bill The Cat. A hard drinking, hard drugging cat. He feeds on popularity and will go to extremes to get it. This has, in the past, ranged from becoming John Belushi to being the lead singer in DeathTongue to starting a cult to running for president to becoming a televangalist. In general his schemes give him temporary fame but then eventually fail, either because Bill dies or fucks up in some spectacular way.
Donald Trump. The main bad guy of the strip. Eventually becomes part of the Meadow when he gets cancer and to save his life has his brain implanted in the body of Bill The Cat. Bill's brain is still there. Evenutally Trump's brain is put back in a human body, but some of Bill's brain goes to that body and some of Trump's brain remains in Bill's body. Therefore as of now Trump and Bill share parts of each other's personalities.
Opus. A satire of Charlie Brown. A very naive penguin who spends much of the strip looking for his long lost mother. (Her fate is too sad for me to include here, you can look it up.) He's always trying to do the right thing but can be talked into believing almost anything. This lets him become the foil for much of the other characters.
Steve Dallas. By far the most complex character in the strip. Outwardly he is a chain smoking, hard drinking womanizing lawyer. But deep down he's incredibly insecure and mostly just trying to get by in a world he doesn't quite understand. He creates any number of money making scams, generally involving Bill The Cat, that always fail on a grand scale. He is loved by the members of The Meadow because despite his weirdness he's incredibly honest and does care about them. Interestingly at one point aliens temporarily "reverse his brain" and when he suddenly is into being a "Nice Guy" nobody can stand him. Thankfully he eventually becomes normal Steve Dallas again. The running joke with him is that he always fails at being a womanizer and nearly every first date he goes on ends up with the woman throwing her martini in his face.
Ronald Anne. The one truly tragic character in the strip. A little black girl living in very shoddy public housing. She was born on the day Ronald Regan was elected president. Her dad believed in trickle down economics so much she ended up named after Regan. Obviously things did not work out as expected. Her existence sort of represents an early example of calling out White Privilage. The other characters like her but don't notice how bad things are for her or think to help her. For example when they are all filling out their letters to Santa they don't notice her's reads "food."
Oliver Wendall Jones. The flip side of Ronald Anne. A young black kid who is a master computer hacker and a member of the upper middle class. He has nearly zero ethics and his hacking and experiments tend to lead to bad, or at least weird, things.
Rosebud. A basselope (half basset hound, half antelope.) An older female character who is generally unnerved by events in the Meadow. She is constantly worried about "hottentots" - which seems to roughly translate as "troublemakers." Was briefly used as part of Ronald Regan's Star Wars Missle Defense System when The Gipper got the idea that shooting basselopes into space would stop Russian nukes.
Mary Kay. The other ongoing bad guy of the strip. She runs a cosmetics company that does animal testing. Obviously the animals of the Meadow are not down with that.