I found enough information on this Oliver B. Bain, and an Oliver Perry Bayne to distinguish them apart:
The identified 1920 census of Berenice, Butte Co, IA
Oliver B. Bain, age 31, born in Kansas to both parents born in Iowa, farmer
Elsie M, age 31 born in Indiana to both parents born in IN
Homer C, 2 11/12
--The census was enumerated on 2/3 January.So Homer born about Jan/Feb 1917; Buelah about July/Aug 1919.
This Oliver would have been born about 1888/1890.
--This person matches the marriage record of an Oliver B. Bain, born KS, to Elsie M, born Indiana found in the Western States Marriage Index.
The World War I Draft Registration:
Oliver Perry Bayne, born Dec? 29, 1890 in Bartlesville, OK
--Three family trees show this person as born 29 Dec 1890 in Bartlesville, Osage Co, OK to Robert Henry Bayne and Mary Elizabeth Elam.He died 8 January 1960 in Orangevale, Sacramento Co, California.He was married to a "Cobb."They had a daughter Edna Bayne, born 30 July 1915 in OK, died 6 Feb 1995 in San Bernardino, CA.She married Albert Woodson Cottriel and had two children both deceased.
The 1910 Census of Big Bend, Republic Co, Kansas
O.B. Bain, age 21, born in KS to both parents born in Iowa, a laborer living in the home of Shursbaugh?
The 1900 Census of Lowe, Kay County, Oklahoma
Benjamin Bain, born March 19, 1845 in Iowa to both parents born in IL, married 31 years, farm Laborer
Mary L, born March 14, 1853 in Iowa to father born in Germany, mother in Ohio, mother of 14/9 living.
John W, Dec 1882, Amanda E, Nov 1885, Lucy E, Nov 1886,
Oliver B, born Dec 1889 in Kansas to both parents born in Iowa
Clara P, Dec 1890 in KS.
Oliver Benjamin Bain, born in Kansas, married Elsie, had five sons and three daughters.He died May 1966 in Worland, Washakie, Wyoming.Elsie died Aug 1979 in Montana