With just a name and a SSN I'd say thats probably pretty tough to find information. Uncle Bob or Louie might have better advice than me though. You could try writing the records center in St. Louis but I really doubt you would gain anything from doing so - most records were destroyed in a fire several years ago. Soldiers back then had an Army Number for identification instead of the SSN which also makes it more difficult.
Do you have any old patches or other items of his from the war? If so, you could describe them to me or even scan them and email it to me and I'll try to find a match in some of my books. I can't promise anything but I'll look for you.
Are there any stories that have been passed down which might contain unit nicknames? Most (if not all) divisions had nicknames.