It wasn't until almost three months later during a routine blood test that she found out she was pregnant from the rape. Odom had two options: one meant the end of her military career and the other the end of the life growing inside her.
Odom was promised by her superior officers that she wouldn't lose her job if she had an abortion and the military was all she had. She paid for the procedure out of pocket, costing her one-third of her monthly pay.
After the procedure, she was honorably discharged.
"I never gave up on the military. They gave up on me," Odom said.
Now, there's an amendment in next year's defense authorization act that -- if enacted -- will help women like Odom pay for medical procedures such as abortions or emergency contraception in cases of rape or incest.
The issue has been a political football in Congress in the past decade, with opponents arguing that taxpayer money shouldn't fund abortions. Supporters say they are calling for an extension of the current law that allows for U.S. Department of Defense funds to be used for abortions if the mother's life is in danger.
Federal funds can be used for abortions in other areas of government, including in federal prisons and by federal employees.
Retired U.S. Army Maj. Gen. Gale Pollock said denying service women who were raped the option of aborting the pregnancy is "a second wrong on top of a wrong."
"It blows my mind that a woman who is raped in prison has the option to carry the baby or abort and military women don't," Pollock said.
As of September 2011, there were more than 200,000 women serving across all branches of the U.S. military, making up about 15 percent of the services. Without them, Pollock said America would likely have a military draft.
"You shouldn't punish them because we're 20 years behind legislatively," Pollock said.
The amendment proposed by U.S. Sen. Jeanne Shaheen, D-N.H., will go to the Senate floor for a vote during the lame-duck session.
Although abortion tends to be a polarizing topic, the amendment received bipartisan support while in committee with votes from Sens. John McCain, R-Ariz., and Scott Brown, R-Mass. Getting the amendment passed in the Republican-controlled House of Representatives may prove tougher.
While passing the Shaheen amendment would be a huge victory for female troops, the Pentagon still has to address the underlying problem of rising incidences of sexual assaults within the military. The Center for American Progress estimates that 300 service women become pregnant every year from rapes.
In some cases, women are denied prescriptions to birth control before they are deployed because "they're under strict orders not to have sex in combat areas and doctors might think they don't need birth control," said Jessica Arons, director of the women's health and rights program at the Center for American Progress.
Garnering bipartisan and bicameral support for the amendment is more than a woman's issue, said Greg Jacob, the director of the Service Women's Action Network.
"It's an issue of national security," Jacob said. "Going to combat and being afraid of having people in their own uniform assaulting them erodes unit cohesion that affects mission accomplishment."