Hi, not sure if this would be enough for a week, we spent a few days there last summer - catch the ferry to Bygdoy - the museum island - it was fantastic - we saw
~the Viking Ship Museum- 1,000 yr old wooden boats - very busy
~ the Kon-Tiki Museum with the original Pacific Ocean crossing raft
~ the Fram - from the Polar explorations
~ my unexpected favourite - the Norwegian Museum of Cultural History with outdoor exhibits - old houses, a Stave church, brilliant displays on Sami culture, folk costumes.
Back in Oslo there's a Munch museum, though the National Gallery has 'The Scream'; the City Hall (where Nobel Prizes are awarded) is a fantastically decorated building; and the Nobel Peace Centre which had very interesting displays and a great collection of inspiring post cards.
We did all of this through the Oslo Pass which covered ferries, transport in quite a wide area (not the airport), museum entrances, a couple of swimming pools, and other discounts. We read about it in the Norway Lonely Planet, or you can try www.visitoslo.com hope that works.
The long days and late sun was great, accommodation was good value with excellent breakfasts, there was a heat wave (30 C) so the city authorities filled the empty fountains with water so people could paddle and cool down - very impressed!
Hope this helps - I'd happily go again.