Traveling to Oslo

Since you need to pick up a car in Oslo, I'd consider flying. SAS and Norwegian have good prices on flights if you book in advance.

We flew Norwegian Air Shuttle--1 hr. and $71--in September.

Do you think you need a rental car for travel in Oslo, or for travel beyond Oslo on you arrival?

If you need the rental car for travel outside of Oslo, fly to OSL Gardenmoen and rent a car at the airport but don't drive it into the city. Parking could be an issue if you are not on a reimbursable expense account and Oslo has a congestion toll:
http://www.visitoslo.com/en/transport/by-car/toll-ring/

Prices and payment You are charged every time you drive into the city.
The price is currently (February 2016) 32 NOK for a max. 3500 kg car.
You do not pay to drive out of the city.

Oslo's toll plazas are automatic. All vehicles shall drive through
without stopping. If you have an AutoPASS tag (subscription), you will
be charged according to the AutoPASS agreement.

For vehicles without an AutoPass tag, payment is made after passing.
The vehicle's registration number is photographed upon passing and the
owner will receive an invoice by post. Please note that it can take
2-3 months before the invoice is issued.

If for some reason you take the train into Oslo Sentrum, you could continue from Oslo S back to Gardenmoen for the airport rental concession after you complete your business within the Oslo central area. NSB fare is 92 NOK each way.