You might try locating the obituaries for her parents and siblings.I believe the following are a match, from the "Illinois Deaths and Stillbirths, 1916-1948" index.Burials are also listed on the City of Galesburg's cemetery site.
Emma Ekstrom, born 26 February 1842 in Sweden, daughter of Mr. Stahl b. Sweden.Wife of Swan Ekstrom.Died 8 February 1919 in Galesburg, Knox County, Illinois.Buried in Linwood cemetery on 8 February 1919.
Swan G. Ekstrom, born 26 February 1831 in Sweden.Parents unknown.Husband of Emma Louise Ekstrom.Died 1 April 1924 in Galesburg, Knox county, Illinois.Burial 3 April 1924 in Linwood cemetery.
Frank D. Ekstrom, born 12 December 1882 in Warren county, Illinois, son of S. G. Ekstrom b. Sweden and Emma Stohl b. Sweden.He died in Galesburg, Knox county, Illinois on 27 August 1937, with burial in Linwood cemetery on 29 August 1937.No spouse listed; occupation was soft drink dispenser in Davenport, Iowa.
Anna Elizabeth Ekstrom, born 16 August 1877 in Henderson Grove, Illinois, daughter of Swan Ekstrom b. Sweden and Emma Stohl b. Sweden.Wife of Peter Nelson.Died 7 December 1946 in Galesburg, Knox county, Illinois, with burial in Linwood cemetery on 10 December 1946.
I don't have online access to Galesburg newspapers during that period.You might try the Knox county website.Also, they might have naturalization records on file at the Warren county courthouse, with copies at the Warren County Public Library.I would like to follow up on these for you, but I don't know how soon I would be able to do so.