There is one mention of an Elihu Murray in the Hampshire County Probate Abstracts 1768-1791. Page 33: Will of William Murray, yeoman, of Amherst, written 22 Oct. 1779 and probated 5 July 1784. "Son" Seth Murray is listed as executor. Also named in the document are "daughter" Dorothy Adams and "grandsons" Elihu and Elijah Murray.
In the History of Hatfield Massachsetts by Daniel White Wells and Reuben Field Wells, Springfield,Mass. 1910 (handwritten date), p. 190, there are both Elihu and Elijah Murray listed on the "Coat Roll." These men were entitled to an overcoat, having "served at least six months" after April 1775.
Same source, p. 193 both Elihu and Elijah are again found as "Hatfield Men Serving in the Revolution." Elihu Murray, a private, serving in the company of Captain Chapin, enlisted in 1775.
In L.M.Boltwood's 1862 "Genealogies of Hadley Families," p. 101: 1. William Murray, of Amherst, d. about 1784, m. 20 Feb. 1723, Hannah, daughter of John Dickinson of Hatfield. Several children include William (also an Elihu born Nov. 1723.) 2. William, born 30 July 1726, d. about 1762. He married Mercy Scott of Sunderland. Children: Elihu born 13 Oct. 1753; Elijah, born 6 June 1756; Mercy, b. 16 Sept. 1758; Martin, b. 14 July 1761.
I am not related to the Murrays, these were records available to me.