Nimrod Eaves was born around 1839 in Albemarle County, Virginia. Prior to the war, Eaves worked as a free laborer and farmhand at Boonesville in Albemarle County at the home of Rice Keller, a 25-year-old Black day laborer. Eaves married Lucy Ann Goings in March 1861, but they divorced the subsequent year.

Eaves enlisted in the 34th USCT Infantry Regiment on October 13, 1864, at Camp Casey, Virginia, for a period of 3 years. At the time of his enlistment, he stood 5 feet, 5 inches tall, and had black eyes, brown hair, and a yellow complexion. He mustered into Company K as a private the very same day, and was soon sent to Jacksonville, Florida, for service in the District of Florida. Davis and the regiment were primarily stationed in Jacksonville, Palatka, and Magnolia Springs, Florida, until November 25, 1864, when they moved to Hilton Head, South Carolina. Once the regiment arrived, Eaves and his comrades quickly entered into action, commencing an expedition to Boyd's Neck, South Carolina, between November 28-30. The regiment saw combat on the final day of the expedition at the Battle of Honey Hill on November 30. Immediately following the engagement, Eaves and the regiment joined the expedition to Deveaux's Neck between December 1-6. Similar to the previous expedition, the regiment again engaged in combat on the last day, skirmishing with Confederates at Deveaux's Neck on December 6. The regiment soon returned to Hilton Head and transferred back to Jacksonville, Florida, in January 1865. In the midst of this transfer, the army promoted Eaves to sergeant on New Year's Day in 1865. Shortly after his promotion, however, Eaves contracted an illness, and he spent time in the Post Hospital Jacksonville during the late spring of 1865. While in the hospital, he was "reduced to ranks from sergeant" on July 6, 1865, while the regiment remained in Jacksonville and the surrounding area in garrison duty. The entire regiment, including Eaves, mustered out on February 28, 1866, in Jacksonville.

After the war, Eaves worked as both a farm laborer and a shoemaker. On April 1, 1877, Eaves married Lizzie Yancey in North Garden, a small village located southwest of Charlottesville. They had no children together. He unsuccessfully applied for a pension in 1881, failing to receive one due to his inability to furnish the necessary evidence for his claim. He reapplied in 1891 and received a pension of $6 per month for "malarial poisoning and rheumatism." Eaves died sometime in 1898.