Maxwell was born on February 7, 1837 in Franklin, Ohio. Little is known about his youth, but on April 17, 1861, at twenty-four years of age, he enlisted in Company F of the Second Regiment Ohio Volunteer Infantry.
By the American Civil War's conclusion, Ohioan Obediah Craig Maxwell had attained the rank of brevet brigadier-general.
Maxwell was born on February 7, 1837 in Franklin, Ohio. Little is known about his youth, but on April 17, 1861, at twenty-four years of age, he enlisted in Company F of the Second Regiment Ohio Volunteer Infantry. On June 11, 1861, military authorities commissioned Maxwell as a First Lieutenant in Company F. On August 16, 1861, he mustered out of the Union Army, having initially agreed to serve just three months. He immediately reenlisted for three years of duty with a newly constituted Second Regiment Ohio Volunteer Infantry. On August 31, officials commissioned him as a captain of Company B in the new regiment.
Maxwell served with the Second Regiment for the remainder of 1861, 1862, and much of 1863. On December 24, 1862, military authorities promoted Maxwell to the rank of major in the regiment and, one week later, to the rank of lieutenant colonel. He participated in all battles fought by the Second Regiment, including the Battle of Perryville, where Confederate troops wounded Maxwell in the leg. At the Battle of Stones River, Confederates wounded Maxwell in the throat. Maxwell also received a serious wound at the Battle of Chickamauga. Due to these and other less serious injuries, military authorities honorably discharged Maxwell on February 1, 1864.
On March 14, 1865, having recovered sufficiently from his wounds, Maxwell became the lieutenant colonel of the 194th Regiment Ohio Volunteer Infantry. Officials promoted him to the rank of colonel on October 22, 1865 and eventually made Maxwell a brevet brigadier-general effective March 13, 1865 for his meritorious duty during the Civil War He mustered out of the Union Army with his regiment on October 24, 1865.
Upon the Civil War's conclusion, President Andrew Johnson appointed Maxwell to a position as the Internal Revenue Assessor of the Third District. He eventually relinquished this position and moved to Lebanon, Ohio. In 1871, Maxwell became the Captain General of the Knight Templars of Ohio and moved to Dayton, Ohio. Unfortunately for Maxwell, this position paid little, and faced with financial stress, he committed suicide on December 5, 1872. He left behind his wife and two children.
Maxwell was originally buried in Dayton, but his wife, Rebecca Maxwell, had her husband's body exhumed and moved to the Lebanon Cemetery in Lebanon on February 2, 1873.