You have no date of death for William, was he killed in the war? If so, this may be him, listed in the Archives war dead database: PFCWilliam H. Emery ID(Army Serial Number): 32742566 Branch of Service: U.S. Army Hometown: Nassau County, NY Status: DOW (Died of Wounds)
There is another William H. listed, but he is from NJ, and a different rank. This William H. can also be found in the Archives enlistment database (with the same ASN but home listed as Rensselaer County, NY). To access that (and more) info, click the link to the following web page, click the SEARCH button, click the "People" link, click the "World War II Electronic Army Serial Number Merged File, 6/1/2002 - 9/30/2002" link and follow further instructions to search database: http://www.archives.gov/aad/http://www.archives.gov/aad/
You can also send for his Individual Deceased Personnel Files (IDPF). As others in this forum have addressed, the info found in an IDPF can be graphic. If you pursue this resource, you should be prepared for that possibility. Send your request to: US Total Army Personnel Command ATTN: TAPC-PAO (FOIA) 200 Stovall Street Alexandria, VA 22332-0404 Be sure to cite the Freedom of Information Act in your request.
Also listed in the enlistment database are: William F. Milot, ASN 32493095 Everett L. Emery, ASN 32576831 both from Rensselaer County, NY.
I'm not sure about info on Vietnam era vets. Perhaps someone else can help you with that individual.