Hi there, I practically live in Oslo and will try to answer any questions.
Shopping in Oslo isen't really exciting at all, the main shopping areas are Bogstadveien, the area around the main street of Carl Johan (in which you can fin LV), Aker Brygge and Grünerløkka. There are only a very few stores carrying high end brands, but you can get it taxed off there. Most of these stores are situated in Bogstadveien (veien /gate means street) and Hegdehaugsveien. However these streets are busy and crowded both by cars and people! Especially saturdays are bad! And don't really expect good customer service in general, allthough there are exceptions (like COME AS YOU ARE and Vòga).
Clubbing in Norway isen't that exciting either, especially sbecause everything closes at 3 am, and people don't really start going out before 11 12 pm. Then there are endless taxi queues and a lot of drunken people in the streets. However there are some good clubs depending on the music you like of course. I'd just recommend walking around in the busiest streets to see if anything fits you, just stay away from the lower parts of Carl Johan, as there are a lot of fishy people around that area.
Like sweetlove mentioned, in nice sunny weather aker brygge is lovely. It's very touristy though, (maybe not in may), so don't expect to get an exciting or interesting meal at a reasonable price there. (It's not that expensive, it's just not that interesting for that price).
The best restaurants in general in Oslo have a lot of famous chefs working for them, some who even won the bocuse d'or and other world renowned prices.
Bagatelle, Stattholdergården and Le Canard won't disappoint. For a more modern and unconventional take of food try ORO.