Wow! Lucky you! It's a tough ride, but some fantastic sights along the way. Must admit I wouldn't know exact routs to take on a bike though. I've only ever done the trip in a car or on the train. Pretty much every village will have campsites and every few miles you will come across a sign saying "Hytte". These are small cabins with no amenities, but at least warm and dry when the weather turns bad. And they are cheap.
As for things to see along the way.....
Art gallery/studios at Vinstra
Dovregubben's hall at Dovre - a large cave
Reindeer meatballs at Kongsvoll are quite yummy and the farm is beautiful
Look for muskoxen around Kongsvoll as well
If you have time for a break from cycling - whitewater rafting in Sjoa river or at Oppdal.
And once you get to Trondheim....the cathedral is beautiful. And there is a very good coffee shop just next to it called Ni Muser. Picknic on the Munkholmen Island is a nice day out. There are great hikes in the woods all around town. The outdoor museum at Sverresborg is worth a visit and should be combined with traditional Norwegian dinner in Tavern, a restaurant from the 17th century. And if you have time and are not fed up with pedalling, take a detour to Hell and back. The bike ride to Hell is on cycle paths the whole way (by the side of the road, but still out of the way of traffic) and has some very nice views of the fjord.