Strother was born in Martinsburg, Virginia (now West Virginia). He studied drawing under Pietro Aneora in Philadelphia, Pennsylvania from 1829 to 1836 when he became a student of Samuel F. B. Morse in New York. Strother was an artist for The Crayon, the leading art journal of the United States at the time, and a frequent contributor to Harper's Monthly. Most of his early work was comprised of landscapes and other outdoor scenes. His art pertained mostly to Virginia and the Southern United States. Prior to the American Civil War, his art was published in books titled The Blackwater Chronicle (1853) and Virginia Illustrated (1857).
During the Civil War, Strother was commissioned by the U.S. Army and assigned as a topographer due to his detailed knowledge of the Shenandoah Valley. During this time, Strother recorded his experiences in the war which he would later publish in Harper's Monthly as "Personal Recollections of the War." His accounts are considered to be unique and are highly praised for their objective viewpoint. He was involved in 30 battles, though never wounded, and was brevetted brigadier general by the War's end.
After the war, topics of his pieces covered a wider range of subjects. Strother began to make works which commented on politics and race relations. He even sketched a portrait of Chief Sitting Bull. Some of his drawings were merely of individuals and groups going about their daily lives.
Strother ended his career as an artist when he was appointed by President Rutherford B. Hayes to be the General Consul to Mexico City in 1879. He returned to West Virginia in 1885 and died there three years later. The New York Times published an obituary in which it is stated that his name was a household one during his career. Strother is buried in Green Hill Cemetery in Martinsburg, West Virginia.