Justice depends on the crime, I'd say when it comes to Asgardian law or legal processes why not let the citizenry decide what punishment they should have?
For example you get someone who has stolen a wallet the citizens have a vote with a selection of punishments from 2 weeks in jail, 3 months in jail, a year in jail, and so on for about 10 levels of severity, each with revocation of Asgardian citizenship at the end of the sentence, murder however especially premeditated gets life in jail no excuse, manslaughter or accidental but preventable (negligent homicide) death gets a less serious sentence.
You then let the people decide by electronic voting their choice of punishment, but ask for responsible voting, it not only puts the fear of God into any wannabe criminal it also gives the people (who sometimes have more common sense than judges) the final say in the criminals final reward for his activities.
Of course the more severe the crime the different options will be but if ALL criminals know what the final choices are going to be they then have to decide if the time is worth doing the crime?
You then really don't need judges after they have decided the punishments for crimes, and it then becomes a popular activity for those citizens who both have the time (gives the retired and unemployed or stay at home something to contribute to) and gives a confidence boost as those who will feel they have had a say in the day to day running of the community as a whole, but yes you will get those who want to hang someone for transgression no matter how small but I think that people will be sensible in the long run.
But one idea I have had regarding my own idea is that evidence must be provided and all involved should be subject to lie detection (regardless of position, be-it criminal/victim/witness), and it should be clear that all crimes will be investigated and should reported (in the case of rapes or familial assaults if it not reported promptly it can't be acted on) and that any false statement leading to waste of police/legal resources must be punished as well.
The biggest concern I have is that any potential criminals will use the "Human Rights" excuse for not accepting their punishment, I believe that if any criminal wants to commit any act they need to realise they are infringing on the "Human Rights" of their victim and any act against said victim negates the criminals "Human Rights" excuse when punishment is issued.