1- From Oslo to Trondheim by AirStarting around $150/£95, this isn't the cheapest option to get from Oslo to Trondheim (or vice versa), but with a 60 minute duration definitely the fastest. Note that it's cheapest to fly from Moss airport or Sandefjord airport outside Oslo, instead of using Oslo Gardemoen Airport. SAS, Widerøe Airlines and Norwegian Air have many direct flights between Oslo and Trondheim daily:
2- Oslo to Trondheim by TrainIt's a scenic 7-hour journey if you take the train from Oslo to Trondheim, or from Trondheim down to Oslo. The train ticket just about equals the flight price, from approx. $150/£95 for date-flexible round trip tickets. There are 3-4 train connections daily and you can buy the train tickets online.
3- Oslo to Trondheim by CarQuite doable, between Trondheim and Oslo it's a 7.5 hour trip by car. You can take the E6 all the way, going through Ringsaker and Folldal.
The shorter route - road 3 through Elverum and Alvdal - saves you about half an hour of drive time. When leaving the city area of either Oslo or Trondheim on the R6, simply look for road 3 for the shortcut.