Could this be your family? I am guessing that your Alexander's father's name was Nils, therefore Alexander would be Nilson or son of Nils. No explanation for his wife's name/names unless he was married more than once. Immigrants often didn't know the English spellings of their names, and the census takers made mistakes, so there are numerous mistakes on census records. If this is your family I assume the Sweden bithplace was a mistake by the census taker.
Alaxander Nilson, 44 born Sweden, 1870, Huron, Des Moines, IA. farmer.
Greta E. 40 Sweden
Anna 15
Emma 10
John A. 5
Matilda J. 1
Solomon and August Carlson farmhands
All born Sweden
Also in Shirley, Polk Co., MN. 1880 Census
Alexander Nilson, 55, born Norway, farmer
(Gale?) G. wife, 50, Norway
Thore 18 Norway
(Shrine?) G. daughter, 15 Norway
Christine 12 Norway
Anna 6, born MN.
I am so glad I could help. Over the years I have learned to check every spelling I can think of, but I hadn't thought of trying Nelson. I am so glad you did.