Norway would fall under Allied Forces Northern Europe (AFNORTH), under a British Admiral or General but also Danish and Norwegian deputies, which included the Baltics and Denmark. sub commands for Norway would be Allied Command South Norway (SONOR) and Allied Command North Norway (NON)
here's a wikipedia which explains it more clearly
http://en.wikipedia.org/wiki/Allied_...orthern_Europe
wiki doesn't say who commands SONOR or NON, I would guess Norwegians.
Not only would British and US contribute, but Allied Mobile Force (AMF) could be deployed to Norway. Theoretically, AMF would include contingents of US, British, Canadian, German, Italian, Spanish, Belgian and Luxemborg in a brigade sized force. I may be leaving some nations out. Not sure how this would work out in T2k because Spain declares neutrality and Belgium and Italy withdraw from NATO. For what it is worth canon does not mention AMF.
Also, the Dutch deploy the 1st Marine Group with the British 3rd Commando Brigade, and the Dutch 2nd Marine Group is part of AMF. I seem to recall both mentioned in the NATO vehicle guide.
I can't specifically remember which British and Canadian units go to Norway in T2k canon. I think 3 PARA and another light infantry battalion from the British and a Canadian infantry battalion, if I recall.
If someone has "Boomer" handy, they can check.