Going there
If your preferred airline doesn't take you to one of these cities - try www.sas.no (part of Star Alliance) or www.norwegian.no (low fare airline). Traveling domestic is quite affordable due to heavy competition. The major flow of tourist enters Norway via "Oslo Airport Gardermoen" (Code: OSL). From here you can fly to any airport in Norway. Under You will find a video clip I have made from OSL airport.
Stop over in Oslo?
Spending only 3-4 days? Don't think so. Go directly to one of the other cities mention. But if you still want to go, use the regular train (inexpensive) or the airport express train (more expensive). Do not use taxi as this is very expensive and take even more time to go to city center, You may also take airport express buses. Traveling with train takes about 20 minutes.
The Coastal line
Try out reservation directly on the coastal line: Link
What city to pick?
It depends. The easiest option is to go to Bergen and enter the coastal line there. Going to Trondheim will take you 3 days. You may also take the route the other way.
Going to Tromso and take the line to Trondheim are consider the most beautiful part. Here you will see the best part of northern Norway and during summer time the midnight sun!