Можно ли подрабатывать за границей во время учебы в универе?

нелегальная подработка = риск лишиться визы
трудоустройство = через университетские службы и т. п.

На сайте университета Осло есть вся информация о подработках для студентов.
http://www.uio.no/english/student-life/part-time-work/
Странно, что вы об этом не прочитали, а задаете вопросы здесь. Если вы не тролль, конечно

20 chasov v nedelyu pri vuze
can work 20 hours pr week during their first year of study. When granted the first student residence permit in Norway, students are granted a permit to work 20 hours pr week, and full-time work during the holidays. The part-time work permit has the same duration as the study permit.

When renewing the study permit, the part-time work permit is not automatically renewed, and students must document satisfactory progress in their studies in order to continue to work part-time.
Be aware that it can be difficult to obtain a part time job in order to supplement your budget. There are a limited amount of jobs available for students without knowledge of Norwegian.