Why remain legal?
A legal stay in Norway will make you part of the Norwegian care system. Norway is not an unstructured country where you may just come, do some work for a Norwegian business and be accepted if you are not registered the right way.
If you are part of the care system you get a pension, vacation money, free hospital treatment, unemployment pay and work insurance, etc.
The only nationalities that do not have to be registered in Norway are those holding a Swedish or Danish passport. Norway, Sweden and Denmark are known by the common name of Scandinavia.
Norway is not part of the EU but is part of the EEA (European Economic Area), which gives every EU country and the remaining EEA countries (Iceland, Liechtenstein, and Norway) the 4 freedoms.
The 4 freedoms are free movement of goods, capital, services, and people.
If you come to Norway as a citizen of the EU/EEA you have to register the right way, and then may stay for a certain period of time, also without a job.