Does this Scandinavia trip itinerary make sense?

If you go with this itinerary, I'd rule out the possibility of day trips. Conversely, if there are any day trips you have your heart set on, I'd compensate by seeing one less city (e.g., cutting out either Stockholm or Copenhagen). Two full days in Stockholm and two in Copenhagen is a reasonable amount of time to get the flavor of each city, but just barely. (I have no experience with Norway.)

Thanks! I didn't have any day trips in mind, really. If I were to cut out either Stockholm or Copenhagen, any idea which would be better?

That depends a lot on what you're interested in. If it were me, and I had to pick one, I'd keep Stockholm and ditch Copenhagen, on the grounds that (1) the Vasa Museum in Stockholm is amazing and (2) Stockholm has better skyline views because of its geography (it's 1/3 water and quite hilly, whereas Copenhagen is flat as a pancake). But they're both fascinating cities that are well worth seeing.

While this is not impossible, it is a pretty aggressive schedule. You could cut out any of the cities and have a much more relaxed itinerary, but assuming you would like to see all the places you've listed, I would suggest the following modification:

Day 1 Arrive Oslo; fly to Stockholm
Day 2 Stockholm
Day 3 Stockholm
Day 4 Travel to Copenhagen
Day 5 Copenhagen
Day 6 Copenhagen
Day 7 Fly to Bergen
Day 8 Bergen
Day 9 NiN to Oslo
Day 10 Oslo
Day 11 Fly home

I've been to all four cities on your itinerary, and I think Oslo is the best place to cut a day and add it to Bergen. Plus I think it makes sense to fly out to Stockholm on the day you arrive. (If you can add that to your existing itinerary, you'll be a lot safer in case your flight to Oslo is delayed. Otherwise, leave plenty of time between flights. Alternatively, you could take the train. That way you could potentially use the train to catch up on sleep and overcome jetlag.) That also means one less time to unpack and repack.

Thank you, Lane! Those look like some good suggestions.

Another option is reversing, doing the NiN on the day after we arrive, flying from Bergen to Copenhagen, etc, but I thought it might be better to push that to the end when we've had more time to get comfortable.

If anyone has any alternate suggestions that start and end in Oslo and don't involve renting a car, I would love to hear them. I have never been to any of these places.