It will help if you can find them in census records, to sort out birthdates. It is hard, because it looks like their surname was spelled differently, from Linrud, to Linndrud to Linderud.
I don't know if you are familiar with Norwegian naming patterns. A child's surname was taken from their father's first name, so in Norway, the children of Ole would have the surname of Olesen or Olsdatter. The wife usually kept her surname after marriage. This started to change around 1900, earlier in the city as opposed to rural areas. Then to make things more interesting, families often took the name of the farm they lived on as a surname - I suspect Linrud is a farm name. Usually after immigrating, the whole family took the same surname, whether it was Olsen, or the farm name.
There is a death listed for Ole Arnesen Linrud on www.familysearch.org
for February 5, 1918. https://familysearch.org/pal:/MM9.1.1/FD3M-V97
Now, you can also search for Norwegian baptisms at the family search site. Go to the home page, then pick Central Europe, then Norway baptisms. I searched for an Albert Arnesen, son of Ole, born in 1879, which was his birth year given in the 1900 Minnesota census. Then, when I found him, with father listed as Ole Arnesen and mother and Johanna Pedersdr, I searched for all children of that couple born in the same place - Hedmark.
This looks like the family, based on the names of the children you have. It is not absolute proof, but a good clue to work onhttps://familysearch.org/search/records/index#count=20&q...
This looks like the family in the 1865 Norwegian censushttp://digitalarkivet.uib.no/cgi-win/WebCens.exe?slag=visbas...
I will see what else I can find to verify the information.