If you want a reliable airport shuttle to/from Oslo that is available 24/7 without having to share it with other travelers, go for the private shuttle service at Oslo Gardermoen Airport.
You can reserve an airport shuttle online as either a one-way or round trip transfer.
These shuttles take travelers quickly either from the airport to Oslo - in which case a driver will meet you inside the Gardermoen airport with your name on a sign. If you need the shuttle transfer for when you leave Oslo, choose to be driven from Oslo to the airport (in which case the shuttle driver will pick you up from your hotel):
Oslo Airport Shuttle Pricing & Booking
All drivers of the private airport shuttles in Oslo speak English and are always happy to help with your luggage. You'll be transported to/from Oslo in a Mercedes without having to wait for any other travelers.
You can still change your booked dates/times after booking the shuttle, and there is a 100% cancellation refund offered up to 3 days before the shuttle transfer itself is scheduled. During booking, provide your flight and hotel details (if available) so the airport shuttle can locate you accordingly.
Alternatively, Taxi2 is a Norwegian taxi service available 24/7 via the Norwegian toll-free number 02202. Taxi2's taxi meters give you the price in NOK and in euros and they accept credit cards as well as cash. Taxi2 offers fixed prices on trips to and from Oslo Airport Gardermoen.