The EHIC is valid across the European Economic Area, which includes Norway (even though it's outside the EU).
You should take your EHIC cards and remember to carry then with you. lf you require treatment in a Norwegian hospital, you might be presented with a bill, which you would have to pay before you're allowed to leave.
If you've got the EHIC, you just show this and the bill is waived. If you've only got travel insurance, you'll have to pay the bill (which,depending upon the treatment, could be for a very large amount) and then try to reclaim the money from the insurance company when you get home. The insurance company might refuse to pay out because you should have taken an EHIC with you.
Basically, think of the EHIC as covering the costs of treatment. The health element of the travel insurance really only covers things such as repatriation expenses (if, say, you had to be flown home in an air ambulance). As I've indicated, many insurance companies will not pay out in respect of a bill which you've only received because you didn't have an EHIC.
Chris