How important is it to know the local language?

It is very important to speak either Norwegian or English if you are going to be in contact with Norwegian customers.

More information
The importance of knowing the local language comes down to who your target group is. If you are going to sell products or services to Norwegians, you will need to speak Norwegian or English. It does not have to be fluently but well enough to understand and be understood. This question also depend on which sector your start-up will be in. If you start a small grocery market selling exotic fruit the language skills are not that important. If you are starting as a carpenter, you need to understand what the customer actually would like you to do.

Either way you need to understand Norwegian or English well enough to report taxes and take care of other legal and practical issues.