Rozy:
You've chosen one of the better seasons to come to Oslo; spring will be in full bloom and temperatures should be fairly comfortable (12-15C) during the day.
1. Some of the "must sees" have already been mentioned like the Viking ships and definetely the Vigeland Park. Holmenkollen Ski jump combined with lunch at the nearby hotel or Frognerseteren is ok.
2. Where to eat..
Oslo has one of Scandinavia's two Michelin** restaurants; Bagatelle (+47 2244 6397) if you're in to very high quality cooking and exceptional service Also there's a more down to earth alternative in Palace Grill which will serve you extreme combinations of different tastes, all of high quality, but come early!! (+47 2256 1502 reservations not accepted). Bølgen & Moi is situated about 10min. drive outside of the city center within the Henie Onstad Art Museum, and the restaurant part is great for dinner (+47 6752 1020).

The price level of these restaurants is generally faily high, but in my opinion have a far better price/quality ratio when compared to similar venues in e.g. London, Germany, USA or Italy. Wine pricing will, due to extreme taxes on alcohol, be through the roof.
I believe that the Holmenkollen Stafett (Similar to a national relay running championship through the streets of Oslo) is scheduled for the 7th of May. It is quite a spectacle but also limits freedom of movement by car within the city; beware!
Enjoy your stay.