I'm not sure about the rest of Norway but I can tell you from first hand experience that finding work as an English only speaker in Trondheim is only 1 step away from impossible.
There is no apparent reason for it as apart from people who are really old, everyone can speak or understand English perfectly well, given that it is taught in Schools as the second language and they have had a lifetime of English TV to listen to. You will discover that a big majority of Norway's people are very Nationalistic (even though they claim not not be) and even though there are some really nice people here, as a foreigner you can face some level of bias when it comes to the job market.
When you start to apply for jobs, I'll just warn you up front that in many cases you will not even receive a response, let alone a "I'm sorry that position is now filled, reply". It's more Norwegian to just say nothing than to say no, but you'll get used to that eventually.
If you are anything like me, you'll seethe with frustration as you watch TV shows like Idol etc and see them using English speaking songs, but your English is not good enough to get you a job, hmmm.
Sorry if this all sounds a bit harsh, but I don't believe in sugar coating truthful experiences. I love the place, and have some really great friends here, and a long time Norwegian girlfriend, but unless you arrive here already highly skilled in a vocation which is in high demand such as the oil & gas industry then you're pretty much screwed to be honest, or of course it's ultimately better to apply for work here before you actually arrive.
If you're coming here as an English speaking, independent job seeker then please make sure you have enough money, or financial backing to last a good few months, maybe 6 months plus to live off, as many people land here full of hope and dreams and the Country just sucks you in and spits you out, then you'll go back where you came from, defeated and broke, and worse still the government will show no interest in helping you either, so forget going to NAV for help with any kind of survivability benefits, the most help they will offer you is a bus ticket to your embassy to seek help there (but there is none when you get there either).
My brass tacks survival advice is this, as soon as you get here look up all the local Bemanning agencies (Job agencies) like manpower etc, get registered with them quickly because unless you are "Extremely" lucky, they will be your only hope of finding any kind of work to help you survive. Either that or go self-employed if you are exceptionally good at something, be highly competitive and offer services that others do not, but above all don't be slow in making a move because as others have said, the cost of living here is very expensive! you don't feel it if you are working because the salary is quite high, but being unemployed can eat your cash faster than you would believe, given that a loaf of bread will cost you around £3 etc.
On a final note, I'd advise you to look up "Janteloven" or Jante law, on Google. It is something of an unwritten law which is interwoven into the culture here - It's crazy and nonsensical and holds a lot of Norwegians in bondage, but it can also affect you, so it's best to be aware of it as you get to grips with the culture.