A WWI Message Board will bring you limited results in finding other family members if they are unaware of his WWI service. You need to post to the Williams Message board for more connections.
I do find a Seamore Williams living in Hendrix, Bryan Co. OK birthdate is Aug 26th 1892, filed a WWI Draft registration card June 7, 1917. He ws farm labor for John Wilkerson of Hendrix, OK, no depandants, single, negro, no disabilities, no prior miltary service. Medium Build, Medium Height, Eyes Black, Hair Black, not Bald. He states he was born in Hendrix, OK but Bryan County didn't exist in 1891/92, not till 1907. He was born in Indian Territory. Link to History of Bryan County:
I looked up Seamore Williams with dob and dod and found he is listed as Semore Williams on SSDI.(Social Security Death Index). Since he had a number then he had to file an application and it asks for parents names, including mother's maiden and places of birth. That is if he remembered them when he applied.(My sister-in-law filled out for mother-in-law's SSA application and listed her mother's grandmother as mother.)Here is a link to his listing with another link to print out SS-5 letter to order copy of application. http://ssdi.rootsweb.ancestry.com/cgi-bin/ssdi.cgihttp://ssdi.rootsweb.ancestry.com/cgi-bin/ssdi.cgi
Now in the 1900 Indian Territory, Chicasaw Nation Township 9 I find a Seymour Williams-son, race black b. Aug 1892 age 8, born Indian Terr (IT)/father-Virgina/mother-IT.
If this is your grandfather then send me an email and I will transcribed rest of family if you don't have access to online census data.