I cycled Kristiansand, eastwards, then north through Lillehammer and north through to Trondheim.
Eastwards I cycled through Roros hitting Sweden's Harjedalen, the most boring county in the world (350km of trees).
This however was a welcome releif in that it was incredibly flat.
Personally I would recommend you keep distances short. (I had a 21km climb to Geilo!!!!!) but tunnels are no major problem.
THere were no warning signs on the one tunnel I went through.
With minimal traffic on no ' No Entry signs' I found the air quality reasonable for a fairly long 700m tunnel.
It is possible that the major tunnels are to the west going towards Bergen but I sure it would be easy to thumb a lift through.
Norway had the most breathtaking scenery I have ever come across, though the plateau towards Tronheim does get dull.
Whatevey you choose be adaptable. Accomodation I found no problem but camping was seldom enjoyable with too many mosquetoes.
Good luck however you go.