Seventh of twelve children of John Nesbitt Nash (1786-1864) and Hannah Harriett Abercrombie (1786-1840) of Fountain Inn, Greenville District (County), South Carolina and then the Babb Community of Bear Creek (Hampton after 1873), Henry County, Georgia.

On 27 January 1839 in Henry County, Georgia Elihu married Elizabeth Louisa Adams (1814-1886). Believed to be the daughter of John "James" Adams (1779-1842) and Elizabeth (unk maiden) (1776-unk) of South Carolina and then Stewart County, Georgia, but not proven yet.

Elihu was the first Nash family member to own what is now the Nash Farm Battlefield Park, 4361 Jonesboro Road, Hampton, GA. He sold this land in 1858 to his older brother, Thompson Edward Nash (1811-1889). He then moved his family on the corner of what is now South Mount Carmel Road and Georgia Highway 81, in the Mount Carmel Community of Hampton.

Seven children:

1.) William Perry "Bud" Nash (1840-1923) who married Martha Ada "Mattie" Hale (1842-1892) (settled Hampton, GA, then McDonough, GA, then Atlanta, GA, then Hope, AR);

2.) Mary Frances Nash (1842-1887) who married William Stephen "Bill" FOSTER (1839-1911) (settled Hampton, GA);

3.) Louisa Jane "Lou" Nash (1844-1887) who married John Gillespie GARRISON (1835-1914) (settled Carrollton, GA, then Waldo, AR);

4.) Hannah Caroline "Tine" Nash (1846-1938) who married Minor Gibson "Miney" RIDGDILL (1844-1906) (settled Jonesboro, GA, then Hope, AR);

5.) John Thompson "J. T." Nash (1848-1895) who married Elizabeth Love "Eliza" Clinton (1847-1921) (settled McDonough, GA, Conway, AR, then Waldo, AR);

6.) James Walker "Jimmie" Nash (1851-1867) who died young (Hampton, GA);

7.) Josephine Elizabeth "Josie" Nash (1856-1867) who died young (Hampton, GA).