Found this information about Elijah on an Ancestry.com family tree:

Source Information:United States National Archives. Civil War Compiled Military Service Records E.O. PriceRegiment Name: Truss Company., Barbiere's Battalion Alabama CavalrySide: Confederate Company: ESoldier's Rank_In: Private Soldier's Rank_Out: Private Film Number: M374 roll 36
Barbiere's Cavalry Battalion, Local Defense Troops [Alabama Reserves]Major Joseph Barbiere's Cavalry Battalion was organized in 1864 from several independent companies which had themselves been created as supporting forces for the Conscript Reserves. The battalion served principally in central Alabama during the fall and winter, 1864-1865, and it was first assigned (1 Nov 64) to Armistead's Cavalry Brigade, District of Central Alabama, until January 1865. The unit was headquartered at Wilsonville, AL (Feb 65) and was reported as serving with the Alabama Reserves with six companies ("A"-"F"). It was assigned to, and included in the surrender of the Department of Alabama, Mississippi, and East Louisiana by Lt. Gen'l Richard Taylor at Citronelle, AL, on 4 May 1865. Barbiere's Cavalry Battalion consisted of Companies "A"-"E" (probably Capt. John C. Brown's, Capt. J. M. Clifton's, Capt. Dawson's, Capt. Thomas J. Goldsby's, and Capt. Thomas K. Truss' companies), "F" (Capt. Andrew W. Bowie's), and "G" (Capt. P. L. Griffitts)
Affidavit requesting Civil War PensionNannie Price, Pike County, Arkansas (widow) of E.O. Price (August 23, 1930) born December 15, 1839 ... "I am the widow of E.O. Price who served in the army of the Confederate States being a member of Thomas K. Truss, Captain, Regiment of Alabama Cavalry from the State of Alabama ... that he was honorably discharged ... from such service on or about the end of the war as he served until the end of the war and then came home ... my husband died (the) 5th day of December 1902. I further state that Elijah Oliver Price and E.O. Price is one and the same person and that my husband enlisted in Elyton, Alabama." Affidavit of Mattie Belcher of Enid, Garfield County, Oklahoma (July 15, 1930) ... that her maiden name was Mattie Love; that she is a sister of Nannie Price whose post office address is Nashville, Arkansas, Route 3, that the said Nannie Price is now about eighty-one years of age; and is the widow of Elijah Oliver Price. Affiant further states that she was acquainted with Elijah Oliver Price on and prior to the date that he married the sister of said affiant, whose maiden name was Nannie Love, and that she was present and witnessed the marriage of her sister, Nannie Love to the said Elijah Oliver Price, and that she knows of her own knowledge that Nannie Price was the sole and only wife of Elijah Oliver Price, that the said Elijah Price died about twenty-five years ago ... that the said Nannie Love and Elijah Oliver Price were married in Blount County, Alabama." Nannie Price died October 12, 1930, Pike County, Arkansas. Witnessed by M.D. Cummings, Sheriff of Pike County, Arkansas, public administrator.