What form of transportation can I take and how long does it take?
Thank you.

During the day, by train, about 7 1/2 hours including two changes.

Take the train back to Koebenhavn H (Copenhagen Central Station). Then you get a train to Gothenburg, and then you change for a train to Oslo. You can get either a fast or a slow train. By memory, I think the fast one is called the X200. The fast one costs almost twice as much. You can also take the train back to Copenhagen Central Station, and then catch a bus to Oslo - one service is available at http://www.eurolines.se and I think there is at least one other bus service also.

There are also flights you can get from Kastrup Airport to Oslo Gardemoen Airport.

It is not necessary to go to Copenhagen. It is easier to just take the ferry from Helsingør to Helsingborg in Sweden (20 minutes). The trains and buses from Copenhagen and Malmö to Gothenburg and Oslo stop in Helsingborg. You can also take the Copenhagen to Oslo boat from Helsingborg (daily at 19:00, www.dfdsseaways.com).

There's also a ferry that leaves from central Copenhagen for Oslo, I think.

Absurd is right about catching the train in Helsingborg on the Swedish side. Does the fast train make as many stops as the slow train, though?