And can one use them to withdraw money or to swipe at stores without any additional penalties?
Or is it advisable to exchange one's dollars for Norwegian krone instead?
BoA Visa/Mastercard credit cards will work fine at Norwegian stores, and BoA debit cards with a Cirrus/Plus logo can be used to withdraw money from ATMs. This is almost certainly more cost-effective than exchanging your money, particularly if you do so in the US.
You will be able to use your cards in many stores, but it is also not too uncommon that Norwegian stores only accept Norwegian bank cards issued for the national BankAxept system. If VISA is accepted, you may have to use a PIN to verify the payment and you may run into problems if you have an old VISA card without chip. Some terminals do not accept cards with only a magnetic strip anymore.
I've often read that VISA cards are accepted "everywhere" in Norway, but I spend a lot of time in Norway and regularly run into problems with my foreign bank cards. One source of confusion is probably that Norwegian banks usually issue cards with BankAxept and VISA integrated on the same physical card and that these cards are commonly referenced to as "VISA cards". Norwegians may hence believe that they pay with VISA at their local store, while the shop actually uses the BankAxept system for payment processing.