Get to play as Goji Rokkaku:
To play as Goji, you first have to unlock the three previous gangs (Poison Jam, Love Shockers, and Noise Tank), and then get a jet ranking on the Grind City stages.

Get to play as Love Shockers:
To play as these guys you have to complete every Shibuya-cho stage with a jet rating.

Get to play as Noise Tank:
To play as the toxic gang, complete every Benten-cho stage with a jet rating.

Get to play as Poison Jam:
You can play as the gang members with the funny monster costumes by getting a jet ranking on ever Kogane-cho Story stage.

Get to play as Potts the Dog:
To get to play as Jet Grind's dog, you first have to complete the game and have all of the previous characters (Goji, Love Shockers, Noise Tank, and Poison Jam) unlocked. Next you have to play through the game again and complete Monster of Kogane before Benten Boogie. After Chapter 2, Noise Tank will challenge you. Win that challenge to get to play as Potts.