I got some help and found my relatives, the Liens, shipped out on the Cunard "Dampsk Hero" to Liverpool. If this listing shows Cunard, does that mean the first Cunard ship is the one they took to America? Also, how long was the Norway --> Liverpool trip? In other words, how much lag should I leave?
They left Trondheim on the steamship (dampskip) Hero in 1884 heading for Yankton in one of the Dakotas. My first guess would be that they would take further passage that would land them in Quebec. Steam travel times and possible connections for that particular voyage of the Hero can be found in various articles and databases on this website. The passenger lists for arrivals in Quebec have been copied to LDS microfilm. While the link I'm forwarding does not deal with ships and passenger lists I think you'll find it to be of great general assistance in your continued search for Norwegian ancestors - http://homepages.rootsweb.com/~norway/articles.html