Oden is actually adopted by Annie shortly after losing her parents to monster and was basically roaming around aimlessly, not eating or drinking anything for nearly three months.

She would be wonderful a forest and had bump a certain white hair female know as the soldier and her group as Annie was a horrified at her state and took her in instantly with Oden being cold and distance when offer food and water though over time she open to them though her and Hanabi didn't get along at all which Annie and Shion still trying to figure out to this day.

Ever since then, Oden was grateful to Annie and made a promise to risk her life for her if she's in danger.