At best Norway would be like Latvia now, at worst most of it's population would be economic refugees.
"Most"? That hasn't happened to any ex-Soviet country, nor any ex-Warpac country. If "like Latvia" means "30-40% Russophone" I beg to disagree.
I consider the question rather a bizarre one. "Joining the Soviet Union" is I presume a misunderstanding, and joining Warpac... unlikely.
What people often fail to realise in these discussions is that the Soviets
did liberate part of Norway. Rather than establishing the Glorious Independent People's Democratic Socialist All-Around Great Republic of the Icy Finnmark Wastes, they did the sensible thing and went home.
As for the Soviet overruning all Norway for some reason, I don't see it. The OTL operation was essentially a pursuit to seal off the northern seam between German forces in Norway and the Finns. A large-scale march down Norway would be a logistical
nightmare. The Soviets can eat the guts out of Germany before they can get halfway down Norway, which is why they wont waste forces that could be fighting the real German armies.
Finland
was a member of the Axis, from the Soviet point of view: the technicalities of military control, intentions, and treaties become less important when a country has invaded your own and been resposnible for the death of your countrymen. This didn't make them any more determined to squash it, which they certainly could have done: what's a few more dead Red Army men to Stalin? "Resources not being directed against the main enemy in order to pursue a useless grudge when I could just sign a treaty removing all threat to Leningrad right now" is what: Stalin had no problems sending his soldiers to their doom, but he wasn't an idiot.
And as for Scandinavian aid, we were taking apart German guns and finding "Made in Sweden" on the parts as it was. There was some ill-feeling, but invading Sweden over it would have been crazy.