Starting to panic

If you are looking for input you should list each day what you and the 3 other people have already decided you are interested in doing and seeing based on the books you are using.

So far I only have Copenhagen for three or four nights. The flight was just recently booked as it was a great price but leaving in 7 weeks, sorry should have said that. Usually do more research/homework in advance. Original thought was to rent a car but it is a 13 hour drive to Bergen and with only 10 days that is two days lost driving.

I agree it would be helpful to be more specific about dates and what has already been decided. Are you committed to round trip in/out of Copenhagen? That would affect my answers to your questions. I did NIN as a long weekend from Copenhagen flying on Norwegian air. However you may have some difficulties depending on dates because train bookings may be sold out as it is peak time of year. That would need to be researched asap so you don't waste time researching a portion of trip that isn't possible.

If you already have your tickets in and out of Copenhagen and you like scenery, I would suggest adding...

--Overnight ferry from Copenhagen to Oslo (in lieu of a hotel room)

--doing Norway in a Nutshell from Oslo to Bergen. This can be done in one long day or split up into two if there is availability

--flying from Bergen back to Copenhagen for your flight home.

If you can also spend a full day in Oslo, you won't regret it.

“Like to see and do all”
The great FOMO. And impossible to do because when you post here for advice you will learn things and suggestions that will increase all the possibilities and thus your FOMO.
The easiest thing to do is create your own plan and not post here for itinerary critique based on the fact that you cannot see it all. Choices are not enabling, they are often crippling.

NiN does sell out. Before planning, best to check availability for that and hotels. High season.

Personally, I’d stick to Denmark. Germany - Schleswig-Holstein has some great spots also- Kiel, Schleswig Viking spots, train fromCopenhagen to Hamburg. Not what you asked, but another idea

If you went to Norway, if you took the DFDS Copenhagen to Oslo ferry that leaves at 1500 and arrives at 1000 next day. So that would give you all day in Oslo then next day Norway in a Nutshell.

The other possible way to get to Norway, if you are also going to explore the north of Denmark is to take the Fjord Line ferry from Hirsthals at 2000, arrives at Bergen Hurtigruten Terminal at 1230 next day (after a brief call at Stavanger). After 1/2 a day to explore Bergen do Norway in a Nutshell next day to Oslo, stay overnight then fly back to CPH next day. (or the 8 hr 30 minute train ride back changing at Gothenburg).

If doing justice to Denmark you should be giving at least a day or two to the north of the country- way up to Skagen with a stop in Aalborg on the way preferably.

You don't say if you are driving or using the train. But by train there is frequent intercity service from Copenhagen to Frederikshavn, change there for the line to Skagen or change a few stops earlier at Hjorring for the line to Hirsthals.
The Skagen and Hirsthals lines are Privatbaner- private railways, not part of DSB.

There is also a 2355 ferry nightly from Frederikshavn to Oslo, arrive at 1000 next day.

I am commited to flying in and out of Copenhagen which is part of the dilemma. We have not rented a car yet but that is our typical plan but if we go to Bergen or Oslo it does not make sense to drive. I never thought about doing Hamburg and some of the other German cities, looks to be a little over 4+ hours. That might be a more feasible option and explore more of Denmark and the Schleswig-Holstein, Hamburg part of Germany. Thank you so much ORDtraveler for bringing it up. Interestingly enough the person that commented on FOMO made me realize that it is not so much about critiquing someone's itinerary as sharing information even a small tidbit can open up new way to approach a trip. Would love to hear more from all.

Years ago I took the overnight ferry from Oslo to Copenhagen. It ran both ways. It was another fun way to travel. On that trip I had flown into Stockholm, took the train to Oslo, then the boat to Copenhagen. From there I flew to Paris.

Even just staying in Oslo you can visit the Kon Tiki Museum, a resistance museum, an open air museum - all using boat and bus. My trip was too quick to add the fjords, but you can decide how you want to split your 10 days.

Don’t miss Roskilde with its Viking Ship Museum and cathedral where the Kings and Queen of Denmark are interred. Roskilde is about a half-hour from København Centraal Station.

Had a similar dilemma pre pandemic, flew in/out of CPH, wanted to see Norway, so we flew to Bergen, did NIN to Oslo, spent another day in Oslo, and took the overnight ferry to Copenhagen with plenty of time to catch our flight back to the US...you have time to do all of the above if you jump on it...if NIN is "booked", you can still catch the ferry that departs Bergen and goes into the Sognefjord all the way to Flam, the scenery is just what you wanted to see, and you can either spend the night there and return to Bergen the next day for more fjord scenery, and then fly back to CPH to end your trip. Bergen is a great place to spend a couple of days, too. Oslo is great, but the fjords are really where it is at for my money on a short stay in Norway.

The point of my story: it can be done...