I'm just gonna tell you the 5 main ones 
1. Crime is a behaviour that is prohibited by the criminal code [ legal definition]
2. Crime is that behaviour that offends the collective consciousness and provokes punishment. I;e something that is immoral would be a crime according to this definition. [Moral definition ]
3) Behaviour which is criminal in a social situtaion which causes a reaction. Living in the real world we usally have to follow the legal code of how we should behave when in public [ Social constructivist definition ]
4. Individuals, instuitations and states denying basic human rights. For example dumping toxic wastes on the ocean, causing air pollution ~people sick~. Also war crimes come under this definition as nobody is allowed to be tortured or persecuted [ Humanistic definition ]
5. Crime does not exist. Only acts exist, acts often given different meanings within various social frameworks. Acts and the meaning given to them are our data. Our challenge is to follow the destiny of acts through the universe of meanings. Particularly, what are the social conditions that encourage or prevent giving the acts the meaning of being crime?
(Christie 2004: 3) [ Social Constructive definition ]
Crime and justice are two different things, justice can be the judgement based on laws but that's not what a "personal justice" would be
And justice doesn't have any 1 complete and universal definition, you can get the definition (and I don't mean in the dictionary) but every individual will interpret it differently
There are legal definitions but not because they are correct but because it would be impossible to work if everyone would use their own definition
As for the ones you listed (in the first post) please attempt to define them because the manga is far from clear on them, you can sort of speculate from the characters' actions but that's not enough