Pity you're not going to Bergen by train - it's a marvellous trip and would get you to Bergen by evening.
However, for Oslo:
1/ There is a direct train link between the airport & main Oslo Station. Trains every 30 minutes for a 30 minute trip.
2/ Most visitors like the Viking Ships exhibit - access via ferry or taxi
3/ Lunch at Hotel Opera (right at the Station). Best Hotel in Oslo that I've stayed at.
4/ After lunch, walk across the road bridge to the new Opera House and take a tour (including walking over the roof)
Good luck
Dave