In those various US censuses it was interesting to note the ages and listed birthplaces for the children of that family. One middle child was born in Norway -- the others appeared to have been born in New York. Nils and this wife (or perhaps an earlier wife) must have been in the US earlier than the immigration dates listed.
I've heard others discuss the many immigrant Norwegian who were in Brooklyn. This was years ago and I was not listening closely because of my lack of personal research interest in the area. They were talking about the records of Norwegian-Lutheran churches which were in Brooklyn and how valuable they had found the information they had gained from those... You might make efforts to search for where those records are now.
The 1890 US federal census was almost completely destroyed by fire. I've never heard of any portions of the 1880 US federal census being missing - there are several websites which can be used to search the 1880 census.