Sue, I looked in my census books for the Edwards you listed in your request. I did not find Walter in the 1850 or 1860 Belmont County census. I did find Elizabeth Edwards in the 1860 Belmont County Pease Twp.
Elizabeth Edwards age 60----Va.Widow Willie age 10---born OH
I did not find Elizabeth in the 1870 census.
Is there another first name that could be a starting point in the line you are requesting??
Sorry couldn't be of better help. Roxann Hoover firstname.lastname@example.org