I tried to check this, but the tariffs are apparently only available to members of the relevant Unions.
I see Kraken has given you a figure and he should know, being active in the business.
(Not an “Oil crises refugee”, like me)
You are right, there are not much barge traffic along the Norwegian coast, at least not in any regular trade. Nearly all coastal shipments goes by ships in some form, even sand and gravel etc. Most are now either specialized pallet carriers, or multi-purpose vessels carrying both Containers, palletized cargo and heavy/bulky cargo.
There are also a lot of vessels engaged in the Fish Farming business. Fairly large vessels carrying feed, live fish for slaughter and smolt to restock the pens. Smaller boat doing net cleaning service, de-licing and inspection by diver and ROVs are also a major business. All are very specialized vessels.
PS> I have posted pictures of some of these vessels in the Pictures of Ships thread FYI.
Tugs and barges are mainly used for transportation of hull sections. offshore modules and other such items, both along the coast and from other places in Northwest Europe. Towage of complete hulls from Poland, the Baltics Romania and Turkey and scrap ships the other way, is also done by tugs. (Many are not Norwegian., though)