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You should try the hotels surrounding the airport. Radisson Blu has a luggage storage room but you will probably need to be staying there to gain access and will probably need to pay a fee to leave for 1 week. https://www.radissonhotels.com/en-us/hotels/radisson-blu-oslo-gardermoen-airport/services.
Another option – if there are six of you. Book the cheapest room close to the airport for 7 days. Say you get something for 75 euros a night (525 euros for the week). That’s 87 euros each for storing your bike. It’s over 20 euros a day to rent a large locker in Gardermoen airport so that would be over 120 euros a day if the lockers were big enough for your bike boxes. Here is a list of the Hotels near by. There is usually a bus service to the hotels close by.
