He attended Prairie View College before becoming a letter carrier with the United States Postal Service (USPS) in 1950 in Orange, Texas.

He also became the first African American elected as a city official when he served on the Orange school district board starting in May 1965.

Odom became one of the first African American postal inspectors in the country in 1967, the same year he was transferred to Los Angeles.

He was raised in the freedom colony of Shankleville, Texas, which was established by his ancestors, James ("Jim") and Winnie Shankle.

The Odom family were subsistence farmers, raising cows, chickens, and pigs and growing crops for food.

Odom's father worked as a carpenter and community undertaker, and his mother maintained a small general store across the street from their family home.

In 1950, Odom became a letter carrier with the United States Postal Service (USPS) in Orange,[5] and earned supplemental income through sales jobs.

The Odoms were active in their community, helping to establish a kindergarten and preschool for black children and participating in the local parent-teacher association.

[8][9] While he was a member of the city council, he worked on transportation, mobility, and redistricting issues facing Arlington.

[14] Incumbent mayor Richard Greene had served in office for a decade when he announced that he would not be seeking reelection in 1997.

I plan to run a clean and positive neighbor-to-neighbor campaign with a simple theme: Getting Results For Arlington."

Odom outlined a 10-point plan for his future administration, which included improving traffic and mobility, reducing crime, encouraging public-private partnerships, addressing unnecessary spending, and economic development.