Ōdera was born in Satsuma Domain (present day Kagoshima Prefecture), as the second son of a samurai in the service of the Shimazu clan.

During the Battle of Toba-Fushimi, he fought alongside fellow Satsuma clansmen Yamamoto Gonnohyōe and Shibayama Yahachi.

Ōdera has praised by French military observers by his cool demeanor when under fire, calmly smoking a cigarette while enemy bullets fell all around him.

While leading his troops during the Battle of Weihaiwei in the First Sino-Japanese War against the land fortifications guarding the naval base, his position was hit by shrapnel from an artillery shell fired by the Beiyang fleet cruiser Jiyuan.

Ōdera was posthumously promoted to 3rd Court rank, and his son was ennobled with the title of baron (danshaku) under the kazoku peerage system.