Planning the EPIC road trip!

I'm very jealous… Norway is top of my list for places I want to visit.
It's up to you if you want to spend time in Oslo. Two weeks will go by fast, so if it were me I'd stop for maybe one night, probably on my return trip to Gothenburg/Copenhagen.
You kind of have to decide how far north you want to travel, because this could determine how much of southern Norway you explore. The Stavanger area has some epic Instagram spots including Preikestolen and Kjeragbolton. Further up towards Bergen is Trolltunga.
I'm glad Bergen is on your list. I think it's the most picturesque and interesting city in Norway. If you're driving there from Oslo, you can stop in Flam and Gudvangen (both situated on arms of the Sognefjord). Check out Norway in a Nutshell, they have great recommendations for self-guided driving tours.
North of Bergen, Geiranger, Alesund, Andalsnes and Trondheim are all good destinations.
One of the biggest draws for me in Norway are the Lofoten Islands in the far north, above the Arctic Circle. You could easily spend a week alone here hiking, kayaking, etc. You may not have time to drive all the way to the North Cape (Nordkapp) and back, but if you want the bragging rights of having been to the top of the world (or at least top of Europe) this is the place to go. I'm not sure if there are Sami in Norway, I know they inhabit the far north of Sweden and Finland, but you might get a little taste of their culture in this region. (You can find accommodations in Tromso if you make it this far). 
Accommodations can be pricey, especially in high season. Do your homework.
Best of luck and happy trails to you. Would love to hear about your trip after you get back! It'll help me plan mine.

My first reaction when I read this type of trip is:
1. It will take a long time, due to transportation time. A trip from Oslo to Bergen will take about 7-8 hours pure driving. Bergen Åndalsnes will take 9-10 hours. (Times were accurate about 10 years ago when I lived in Bergen and visited my parents in Oslo, and a very good friend of mine in Molde)
2. I don't know how your route is. Are you going from Gothenburg to Copenhagen and then to Oslo with a car? In that case I'd recommend taking the DFDS ferry from Copenhagen to Oslo, having your car on it. If not, I'd recommend not hiring a car before you get to Oslo. Take the train from Gothenburg to Copenhagen and fly/passeengerferry to Oslo. Hire a car in Oslo for the rest of the trip, leaving it in Bergen. Hiring a car in Sweden or Denmark to leave it in Norway will cost you a higher fee, since the company will have to return it to the original country.
2. When you mention hiking: What kind of hiking are you looking for? Camping overnight with tent, or walking from hut to hut (absolutely possible through den Norske Turistforeningen (DNT) (see their webpage).
3. Cities and nature worth exploring in Norway: Oslo (worth several days), Borgun stavkirke, Stallheiskleiva, Bergen (Tyskebryggen, Rosenkrantztårnet, Hanseatsk museum, Fløyen, just from the top of my head), Geiranger, Trollstigen, Åndalsnes.