Since 1867, the police in a number of districts have kept lists of emigrants with their names, home address, date of departure, destination, and - in some cases - name of ship.
These lists may often prove to be the best starting point for your inquiries. They are usually kept at the local police station, but the oldest lists of Oslo, Kristiansand S., Bergen, Ålesund, Molde, Kristiansund N., and Trondheim have been transferred to the regional archives. The regional archives in Oslo also contain emigrant lists from the White Star Line's agent for the period 1883-1923. The Stavanger emigrant lists were destroyed by fire, but copies of the lists 1903-1929 are found in Riksarkivet, and they are being computerized by the Digital Archives.
It should also be noted that "domicile" is frequently not identical with "place of birth." Since many emigrants moved to a town some time before they left Norway, their domicile may be listed as, for example, Christiania, Bergen, or Stavanger even though they were not actually born there.
Since 1810, lists of passports (passprotokoller) have been kept by the police, and the oldest ones are now in the regional archives. Such lists do not contain as much information about emigrants as the emigrant lists normally do, but they can often provide the birthplace, the age, and the destination of the emigrant. In Norway, the requirement to have a passport was abolished in 1860, making the post-1860 lists of passports less important to researchers.
The available types of emigration records online you can see in the picture below
As you also can se there are 88 different databases to search in. Not all are equally useful for the genealogist. Some are there for the statistician. But be sure to browse all the material or you may miss some info.
Some info about the emigration lists from Oslo/Kristiania on the list below