Agree, it's helpful to have as much identifying information as possible - and very important to speak up, to post again in your thread.
The following family is from Sør-Trøndelag fylke, where Trondheim is. Øksendal is in a different fylke.
Emigration (candidate to be Oscar)
Departing Trondheim on the SS Tasso
Destination: Onalaska, Wisconsin
....ticket paid in America
Oline Sæther age 30
Peder Sæther age 9, son
Oskar Sæther age 7, son
Dorothea Sæther age 4,5
Lars Sæther, age 3http://digitalarkivet.arkivverket.no/gen/vis/8/pe00000000083...
(Click"Neste" to see each person in turn)
After changing ships for the transatlantic voyagehttps://familysearch.org/ark:/61903/1:1:KGKY-MDZ
Possibly the father Peder departing earlier, herehttp://digitalarkivet.arkivverket.no/gen/vis/8/pe00000000069...
Same trip, after transferring ships in Englandhttps://familysearch.org/ark:/61903/1:1:QVS2-3LX9
1900 US census
Onalaska, La Crosse, Wisconsin
Olena Sather b Feb 1854 Norway, to USA 1884
Meridien, Whatcom, Washington
Oline (Olive) with sons Lars (Louis) and Rudolphhttps://familysearch.org/ark:/61903/1:1:MGJQ-DDW
An indication here that Olene's patronym was probably Olsen.https://familysearch.org/ark:/61903/1:1:XRGL-CNM
1900 census says Dorothea was born July 1878 in Norwayhttps://familysearch.org/ark:/61903/1:1:MMVC-MGB
Dorothea Sather Fletcher in
1910 in Onalaska, La Crossehttps://familysearch.org/ark:/61903/1:1:MPKG-QQF
1920 in La Crosse, La Crosse, Wisconsinhttps://familysearch.org/ark:/61903/1:1:MF21-Z5K
The above Dorothea was born 1878, making her a match to the sister of the candidate Oscar. She died 1947 and Chester Charles Fletcher died 1948, both buried in Onalaska:http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=Fl...
Following one line of descent for the above Dorothea, a candidate to be son Harold Fletcher in La Crosse:
Geni tree. Not complete enough info in this thread or in the tree to confirm whether this is your Sather family, but it seems to be. There might be a tree on Ancestry as well...https://www.geni.com/people/Oscar-Sather/6000000000563718191
Other siblings could be followed. For example, in 1910 Richard was in Edmonds, Washington; then to Everett, Washington; to Petersburg, Alaska in 1930; died 1949 in Santa Barbara, Californiahttps://familysearch.org/ark:/61903/1:1:29JS-526