There are several types of transportation you can use to get from Copenhagen to Oslo and back, and each option has its own pros and cons that may make it more or less suitable for you to get from Copenhagen to Oslo or vice versa.
1- Copenhagen to Oslo by AirWith a flight time of just over an hour, flying directly from Copenhagen to Oslo is a time-saver. The pricing of this option is higher than bus fares, though, but still very affordable from around $150 / £90:
2- Copenhagen to Oslo by TrainA great option to get from Copenhagen to Oslo or from Oslo to Copenhagen within about 8 hours. Taking the train to Oslo (or Copenhagen) is a very comfortable and reliable method of transportation. It's more expensive than driving or taking the bus, though. Online booking of unlimited multi-country train passes available at RailEurope.com.
3- Copenhagen to Oslo by CarIf you'd like to rent a car to get from Copenhagen to Oslo, you have two options. The fast option is a 600 km (7 hr) drive using the Øresund Bridge and going north on the E20, turning onto the E6 toward Oslo in Göteborg. Quick and pretty, but costs gas and bridge toll.
The second option is a 800 km (10 hr) drive from Copenhagen to Oslo across Århus and Ålborg in North Jutland (E20 west/E45 north). Take the ferry from Hirtshals (or Frederikshavn) across the Skagerrak to Larvik and drive to Oslo from there. A scenic drive, but you'll have to submit to ferry schedules. More ferry options below.