I never got your first message. Thanks for checking back.
This is what I found.
1850 Saline, Il, p. 34b
James E. Odam, 27, cabinet maker, Tn
Vienna, 18, Tn
1860 T9, R6E, Harrisburg, Saline, Il, p. 891
JE Odam, 37, Cabin(et?) Maker, b: Tn
Vianna, 27, IN
Sarah E., 8, Il
Viola C., 4, IL.
Wm. N., 1 month, Il
Frank Fly, 19, laborer, Il
1870 Harrisburg, Saline, p. 395a
Elias Odum, 47, carpenter, Tn
Vianner, 37, In
Clemintine C., 15, Il
James P., 8, Il
Letha or Reba ? can't read it, 5, Il
Elborn, 3, Il
Sarah Goodrich, 17, Il
Couldn't locate them in 1880, but I wonder if this family is related?
1880 Harrisburg, Saline, Il, ed 110, p. 108a
K. Odom, 64, Tn/Tn/Sc
Faithie, 58, Tn/Nc/Nc
Wiley, 23, Il/Tn/Tn
Vina, 17, Il/Tn/Tn
Sammy, 8, IlJulia, 4, Il/Il/Il
John, 3, Il/Il/Il
George, 1, IL/Il/Il
1910 Equality, Gallatin, Il ed 25, p. 17b
John Odom, 39, first marriage, married 13 yrs., Il, blacksmith
Zora, 39, married twice, 13 yrs, she has had 6 children, four living, Il
Reba, 4, Il
Alvina, 3 mo., Il
Couldn't locate them in 1920
1930 Tyrone, Franklin, Il, ed 41
404 W. 6th St.
John E., Odom, 56, he was 30 at his first marriage, Il, Porprietir of Retail Store
Zora A., 58, 15 at first marriage, Il
Alma N., daughter, 20
Lyle Kingman,son-in-law, 27, 19 at first marriage, Il, Lampman in Coal Mine
Reba,daughter, 23, 15 at first marriage, Il
Berrell,grandson, 6, Il
The following is from the Saline Co. Genweb site.
1910 Prairie Framers and Breeders directory
Orby B. Odum (Neppie Davis) ch: Charles, Bessie, Rosalie, Quintoen, Carriers Mills R1, tenent 80a, D.B. Odum (1887)
Wiley Odum, (Anna Empson)ch: Agnes, Frank, Blanche; Samuel Odum brother. Harrisburg R2, owns 43a, (1857)
Saline County Illinois
Whereas, a jury this day sworn before me, according to law, to inquire of the death of John Endicott did, by their verdict, fond one Edd Odum to be the unlawful slayer of him, the said John Endicott. You are, therefore, in the name and by the authority of said people, hereby commanded to receive the said Edd Odum into the county jail of said county (Saline) and him there safely keep, to be dealth with according to law. Hereof fail not. Given under my hand and seal, at Harrisburg, Ill., this 27th day of January 1919. F. H. Ozment, coroner of Saline County.
In the matter of the inquisition on the body of Hazel Odum deceased, held at 2 miles northwest of Carrier Mills on the 30th day of April 1913. We, the undersigned, Jurors, sworn ton inquire of the death of Hazel Odum on oath do find that she came to her death by defects of the circulatory system. W. H. Russell, foreman, J. D. Allen, Geo. Hargis, H. R. Thornton, J. W. Fife, Thos. Buckner.
I'm not able to answer why John moved to Union Co., Ky in 1904. Union was right across the border from Saline and Gallatin. Maybe he went for work? According to the 1910 census John and Zora married in 1897, so I would look for that marriage record in either Saline or Gallatin Co. When writing to Saline you might also inquire about a will and/or probate for James Elias Odom. That may give you information about his children.
Good Luck and if I can look for something else for you, let me know.