Are there any accommodations between Flam and oslo to break up a car journey?

Finse is the only location that is possible, I think. It is the highest train station in Norway and maybe in Europe. It is not known for its good weather. There can be snow there even during the summer. It looked sort of interesting when I took the train from Flam to Oslo, but I didn't stop.

You can’t drive a car to Finse.

Suggestions depend on route.
If you choose Flåm – Voss – Eidfjord and Rv7 over Hardangervidda, there are
hotels in Ulvik and Eidfjord or mountain lodges on the plateau like “Halne fjellstova”.
If you follow E16, then a detour to Beitostølen at Ryfoss is an option.

If you choose Fv50 (Aurland – Hol) or Fv52 (Hemsedalsfjellet), then Gol, Golsfjellet or Geilo are places to look.

Oops, I did not notice the person was driving. Yes, you are right. You cannot drive a car to Finse.

Thanks for correcting my bad information.

Jjzz- I did not realize there were 3 possible routes. We decided not to go through Lom, because of added mileage. We did see a Radisson Blu in Beitsolen and were planning to round trip on E16.. Is there any advantage to either of the other 2 routes you mentioned?

Gol possibly? I think it has a stavkirke too so nice for a few pics...

We rented a cabin for three nights in Beitostolen last summer. Very nice area:

http://www.knuts-hyttegrend.no/

All routes have their advantages - I would certainly do a round trip rather than back and forth on one route. The real question is if you have a car and thereby access to so many places why are you going to stay in Flåm with its hordes of cruise tourists? Consider Balestrand and places on the way there. http://www.visitnorway.com/uk/ and then maybe Lom wouldn't be a bad choice for one direction.