Not sure which ODOM group you are descended from.There is James ODOM, Jr (some give James W. ODOM) md Mary CRISP who had a large descendancy in Cannon Co., Tennessee...many moved to Texas.
One of his sons was Jehu McAdoo Alonzo ODOM, Sr. (1820-1898) who married 21 October 1839, Wilson Co., TN to Mary Granger LAX (1819-1905).
Jehu McAdoo Alonzo ODOM (Sr), son of James ODOM, Jr. and Mary CRISP; born 17 October 1820 (tombstone), Wilson Co., (now Cannon Co.), TN; died age 77 on 30 January 1898 (tombstone); buried at Waxahachie City Cemetery, Waxahachie, Ellis Co., TX.>>>SEE FIND-A-GRAVE MEMORIAL #33177772 and his wife's link is there too.
FAMILY NOTES SAY: November 1871 - MOVED. Jehu ODOM, wife Mary LAX and family left Cannon Co., TN and arrived with their family in Texas 'on Nov. 17, 1871' and settled in Ellis Co. 'five miles from Ennis on the east side of Mustang Creek.'This couple seems to be the first of the ODOMs to leave Tennessee and settle in Texas.
My observation: Their daughter Nancy ODOM who married George Washington VAUGHN, I believe left Cannon Co., TN for Ellis Co., TX before the parents, based on the birth location of one of their children.
Jehu ODOM and Mary LAX had ten (10) known children: Frances E. ODOM, Nancy M. ODOM, William H. ODOM, Lucy A. ODOM, James W. (or A.) ODOM, Mary S. 'Molly' ODOM, Sarah L. ODOM, Theodosius E. ODOM, Alonzo? "Lon" ODOM and Jehu McAdoo Alonzo ODOM, Jr.
All this to say that Jehu is sometimes referred to as "J. M. ODOM" as is shown on his tombstone at Waxahachie City Cemetery.He left Cannon Co., Tennessee and moved to Ellis Co., TX, so would fit your criterea of Odom, TX.