Norse Atlantic Airways has round-trip flights from New York (JFK) to Oslo (OSL) for $341-$370, NONSTOP. Flights in May. Departures on Monday and Wednesday.
Some small OTAs on Skyscanner and Kayak have this for as low as $335; which is cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.
Norse Atlantic is a budget carrier. Fares do not allow for a free carry-on bag. Only a small personal item (17 x 14 x 8in) like a Jansport SuperBreak backpack is allowed without additional fee. You can avoid paying for seat selection if you accept the randomly assigned seat prior to boarding. Checked and carry-on bags cost between $45 and $70 each-way, depending on weight and size.
Click for more details and booking links Nonstop Flights: New York to Oslo $335-$370 r/t [May] – Norse Atlantic Airways / Skyscanner