I followed the daughters Anna and Agnes and made some progress.
1. Anna Andersdotter, born 1851-09-25 in Offerdal
Had an illegitmate son Carl Rudolf Walter born 1882-11-03 in Östersund. Emigrated to North America in 1885. Returned to Sweden in 1900 with Vejt Rudolf Burman and their son Andrew Gustaf Burman, born 1885-10-10 in Slayton, America (Slayton in Minnesota?) and the aforementioned Carl Rudolf Walter Burman.
Andrew returned to America in 1907 (to work in his uncles store?), while the others remained in Sweden. Anna died 5/8 1924 in Rödön, Jämtland. Vejt Rudolf died 13/12 1924, also in Rödön. Carl Rudolf Walter died 16/8 1933 in Frösö, Jämtland.
Östersund AIa:11b, p. 384
Rödön AIIa:1, p. 147
2. Agnes Andersdotter, born 1854-09-13 in Offerdal
Her oldest child Karl Ludvig was born in 1876. She married Mikael Ludvig Källström in 1878. They moved to Minnesota about 1886. Then to South Dakota, where I found them in the 1900 census.
Lit AI:13b, p. 504 (& p. 511)
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MMR4-PVR : accessed 2 November 2018), Agnes Kellstrom in household of Michael S Kellstrom, Clarno, Orland & Winfred Townships, Lake, South Dakota, United States; citing enumeration district (ED) 214, sheet 3A, family 46, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,241,551.
Their son Nels Gustave Kelstrom married Minnie Otilla Johnson. One of his descendants named "Deborah" posted a message on the Ancestry message boards in 2007 (scroll down):