The main source for research on the family is in the publication: 
"Familien Hagerup i Danmark og Norge by Sofus Elvis, 
published at H. Hagerups Forlag in Copenhagen, 1902

Legatet til minne om Stiftamtmand Edvard Hagerup m/frue.

Hagerupgaarden i Bergen where Edvard Hagerup lived with his family

Gaarden Oevre Oeien in Alvdal, bought by Nicolai Hagerup, born 1736

The family Carlsen from Germany/Denmark

The painter Niels Hagerup b. 1864-1922 lived in the United States

Prime minister Francis Hagerup who handed over power in 1905 to Christian Michelsen
(Hagerup was afraid Russia taking over the Northern part of Norway if Norway became independent of Sweden.  In 1945 Russian troops took their time to leave after "liberating Finnmark".)

Skipet Norge som forliste med emigranter

Gustav Vigeland was a friend of my grandfather Henrik Bergh f. 1879, and he was allowed to use "Wheel of life" as Ex-Libris in his time.  

There is a villain in every family.  Check out Andreas Dedekam Hagerup Gyldenpalm. b. 1777

Other significant sources in looking for ancestors;

Censuses in Norway

Censuses in Denmark

Sweden still has some distance to go before they  have useable data, but there is what they have

Bertling_Marit - Bjarkøy

Munthe

Nordic Genealogy Site (Per Nermo)

Sodemann

The family Ostenfeldt, by Conrad Peter Ostenfeld