The 1900 census looks like George and Martha are his possibly brother? and wife or other relative but not his parents. Highly unlikely that he was born when his father was age 7. (More Odoms in adjacent households)
Found other records, but not parents.
Source: "United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M3VP-3VW : accessed 9 November 2018), Howard D Odom in household of George Odom, Militia Districts 1121, 1145 Ashburn town, Worth, Georgia, United States; citing enumeration district (ED) 104, sheet 45A, family 856, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,240,230. https://www.familysearch.org/ark:/61903/3:1:S3HT-68LS-9ZJ?i=88&cc=1325221
George Odom Head M 30 Georgia
Martha V Odom Wife F 25 Georgia
Zack V Odom Son M 11 Georgia
Dorsey H Odom Son M 9 Georgia
George C Odom Son M 4 Georgia
James L Odom Son M 1 Georgia
Howard D Odom Servant M 18 Georgia
Source: "United States World War I Draft Registration Cards, 1917-1918," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K3PF-TJL : 13 March 2018), Howard Durfield Odom, 1917-1918; citing Geneva County, Alabama, United States, NARA microfilm publication M1509 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,509,387. https://www.familysearch.org/ark:/61903/3:1:33SQ-GYRB-39LF?i=78&cc=1968530
World War I Draft Registration Cards
Name Howard Durfield Odom
Rt A Chancellor, Geneva, AL
Draft Registration Sept. 12, 1918, Geneva County, Alabama, United States
White Male Age 36 Birth March 16, 1882, US
Farmer Employer: John Watson, Geneva AL
Nearest relative: Mollie Odom : RT A, Chancellor
Source: "United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MKQ2-2RH : accessed 9 November 2018), Howard D Odum, Campbells, Geneva, Alabama, United States; citing enumeration district (ED) ED 104, sheet 6B, family 116, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 14; FHL microfilm 1,374,027.
United States Census, 1910 Campbells, Geneva, Alabama
Howard D Odum Head M 28 Georgia/GA/GA married 5 years
Mallie Odum Wife F 26 Alabama/AL/AL
Ira M Odum Dau F 3 Alabama
Mary E Odum Dau F 1 Alabama
Ainier Odum Cousin F 11 Alabama