Bringing a car
The general rules are as follow for bringing a car are:
If you have a permanent residence outside Norway or a temporary residence in Norway, you can import and temporarily use a foreign-registered vehicle in Norway without paying taxes or duties. If you have a permanent residence in Norway, you can only use a foreign-registered vehicle in certain cases.
For further information read the regulations for duties for cars and other vehicles by the Norwegian Tax Administration.
The Norwegian Tax Administration has made a calculator to use when importing a car (or other vehicles).
When bringing a pet
If you intend to bring a pet, you must contact the Norwegian Food Safety Authority and check which requirements and restrictions apply (mattilsynet.no).