W SHEROAN Birth: 5 Apr 1903State Where Number was Issued: KentuckyDeath: 12 Sep 1989
William SHEROAN Birth: 9 Jan 1930State Where Number was Issued: KentuckyDeath: Dec 1973
William SHEROAN Birth: 12 Jul 1945State Where Number was Issued: KentuckyDeath: Dec 1968
W born in 1903 is the right age to have been your grandfather. I don't know how the 1945 one fits in; cousin, maybe. He died in an accident or Viet Nam, I'll bet.
The RootsWeb SSDI http://ssdi.genealogy.rootsweb.com/cgi-bin/ssdi.cgihttp://ssdi.genealogy.rootsweb.com/cgi-bin/ssdi.cgi will format a letter for you. Click on "SS-5". Send it and $27 to the SSA for a copy of the person's SSN application. That will get you their parents, birth place, birth date, occupation and address at the time.
The 1903 W died in Hardin Co. Kentucky. You get 19 hits in Google for Sheroan Hardin some of them genealogy.
Your dad's obituary would help you. You could try for W's, too, with a post on the GenForum Hardin County page.
All of this is useless if you are an Aussie. Please tell me you are an American, the Sheroans you are interested in are inthe US and I didn't waste by coffee break.