The Answer
An outlaw is someone outside the protection of the law, a bandit is someone who cheats/robs, and a crook is a dishonest, untrustworthy person.
Dictionary.com defines an outlaw as “a lawless person, especially one who is a fugitive from the law” or “a person, group, or thing excluded from the benefits and protection of the law”. The latter is closer to the word’s original meaning, since it refers to someone outside the law. One of the harshest punishments in many societies throughout history was taking away someone’s legal rights and protections. It almost always resulted in the subject’s death, usually at the hands of other civilians.
Bandit is a more general term, and applies to anyone who commits crimes (especially those who do it regularly). Although bandit can generally mean a criminal, it’s usually used to describe people who rob/steal from others. Even there, the definition is a bit lenient. While bandits usually use force to threaten/rob others, bandit also applies to those that cheat/con others out of their money.
Interestingly, the word bandit has similar origins to outlaw. They both refer to someone who is banned, excluded, or maybe even, outlawed from society.
Crook is more of a judgement of a person’s personality, and not all crooks have committed crimes. It means someone who’s dishonest, and fits well with the cheater/conman interpretation of bandit.
The noun crook entered English in the 13th century as a way to describe the long tool with a hook at one end. It later took on the meaning of “petty criminal.” You can use crook as an informal way to describe someone who is dishonest. A crook is typically involved in minor or nonviolent crimes; you wouldn’t use the word to describe a murderer, for example. A con man or someone committing fraud could be called a crook.
In theory, someone can be an outlaw, a bandit, and a crook. But outlaw refers to their position regarding the law, bandit refers to the crimes they’ve committed, and crook refers to their personal qualities.