This will prove to be only a partial answer but it will get you started.
First of all, the names of the ships in question are SS WILLIAM GRAYSON and SS JAMES TURNER, not "USS" in either case. USS stands for United States Ship and refers only to commissioned ships in the U.S. Navy. Both WILLIAM GRAYSON and JAMES TURNER were civilian merchant marine vessels that were never a part of the Navy. SS means "steam ship" which describes the type of ship (or more specifically the type of propulsion) for both ships.
I have found records for an Edmund Winslow Nutter as the Armed Guard commanding officer on two voyages aboard JAMES TURNER in 1943. I did not find records for him aboard WILLIAM GRAYSON, which I attribute to the fact that the online sources available to me are not comprehensive. Specifically, the two records I found came from a search of the subscription website Ancestry.com (www.ancestry.com), which contains databases of the names of crew and passengers aboard merchant vessels that arrived in certain U.S. ports of entry. These records are particularly extensive for the port of New York but less so for other ports. It is possible that WILLIAM GRAYSON departed from and/or arrived at ports that are not well represented in Ancestry.com's records.
(FYI, periodically Ancestry.com has discount deals on subscriptions. You might consider a short, low-cost subscription to make the same searches I did or to make others. Subscription information is available on the website's home page.)
This is the detailed description of the two (consecutive) voyages aboard JAMES TURNER in which I found your grandfather.
Voyage #1: JAMES TURNER departed Boston July 4, 1943, arrived Halifax, Nova Scotia, July 6; convoy BX61.
Departed Halifax July 11, arrived Loch Ewe, Scotland, July 22; convoy HX247.
Departed Loch Ewe on unspecified date, arrived Methil, Scotland, July 24; convoy WN457A.
Departed Methil July 26, arrived Hull, England, July 28; convoy FS1178.
Departed Hull August 8, arrived Methil August 10; convoy FN1094.
Departed Methil August 12, arrived Loch Ewe August 14; convoy EN267.
Departed Loch Ewe unspecified date, joined convoy ON197 underway from Liverpool, arrived New York August 27, 1943.
Voyage #2: JAMES TURNER departed New York September 7, 1943, sailed without convoy, arrived Philadelphia September 8.
Departed Philadelphia September 23, sailed without convoy, arrived Hampton Roads (i.e., Norfolk area) September 24.
Departed Hampton Roads September 25, arrived Casablanca, Morocco, October 12; convoy UGS19.
Departed Casablanca October 19, joined convoy GUS18 underway from Alexandria, Egypt, arrived New York November 6, 1943.
JAMES TURNER was a class EC2-S-C1 Liberty ship, constructed in 76 days by the North Carolina Shipbuilding Company, Wilmington, NC, between July 26 and October 10, 1942. She survived the war and was scrapped in Kearny, New Jersey, in 1970. See http://www.shipbuildinghistory.com/history/shipyards/4emergencylarge/wwtwo/northcarolina.htm and scroll to hull number 22. Also see http://www.mariners-l.co.uk/LibShipsJ-Ji.html#JamesJ and scroll to the name of the ship. Her namesake was James Turner (1840-1915), an African-American educator who was active in Missouri politics and served as minister to Liberia in 1871.
WILLIAM GRAYSON was also a EC2-S-C1 Liberty ship, constructed in 60 days by Bethlehem-Fairfield Shipyard, Baltimore, MD, between July 16 and August 14, 1942. She survived the war and was sold to the Greek government in 1945. Thereafter she was sold and renamed several times, operating under the Greek and later the Lebanese flags until she was scrapped in 1968 in Taiwan. See http://www.shipbuildinghistory.com/history/shipyards/4emergencylarge/wwtwo/bethfairfield.htm and scroll to hull number 2060. Also see http://www.mariners-l.co.uk/LibShipsK.html and scroll to the name KERKYRA. Her namesake was William Grayson (1736-1790), a Revolutionary soldier and aide to General Washington, a member of the Continental Congress from Virginia and later a U.S. Senator from Virginia 1789-1790.
That leaves your grandfather's service in WILLIAM GRAYSON and I'm not able to help you there. But you may be able to obtain a copy of your grandfather’s military service record which should indicate the dates during which he was assigned to that ship. Please see this page from the Armed Guard website: http://armed-guard.com/searchmil.html. In particular see section A.1. Records of Individuals - U.S. Military. You will have to contact the National Personnel Records Center in St. Louis, MO, a facility operated by the U.S. Archives. Provide as much identifying information as possible about your grandfather. The links on this web page will take you to the necessary pages of the Records Center web site. There may be a fee for obtaining the information but the Records Center staff will not begin research without informing you of any charge. In addition to the ships to which he was assigned and applicable dates, your grandfather's military service record may contain such information as enlistment date, discharge date, training, illnesses or injuries, any decorations or medals earned, etc.
Note that someone such as yourself, who is not next of kin to your grandfather, may not be able to obtain his full service record. (Next of kin = parent, spouse, sibling, child.) If there is someone still living in your family who is next of kin to your grandfather, presumably your grandmother, mother/father or an aunt/uncle, it would be best if the request to the Records Center was submitted by that person. You can do the legwork of research, completing forms and otherwise preparing the request but the request should be signed by that person. If there is no longer a person who is next of kin still living, then make the request yourself and hope for the best.
Finally, if you are able to determine the dates during which your grandfather was assigned to WILLIAM GRAYSON, visit the excellent website ConvoyWeb (http://convoyweb.org.uk/hague/index.html) and do a "Ship Search." This website lists what convoys in which a ship sailed, originating and destination ports, applicable dates, and sometimes a bit of information about the cargo of a ship or any unusual event experienced by the ship or the convoy. There will be no information about the crew. You should be able to match up the dates your father was aboard the ship with the whereabouts of the ship during that time. I did a search of ConvoyWeb for WILLIAM GRAYSON and found multiple entries. Of course not knowing when your grandfather was aboard made what I found fairly meaningless, except to say the information exists.
A similar website is http://warsailors.com/search.html, which is not nearly as comprehensive as ConvoyWeb but occasionally has some very interesting details about a ship or a convoy. I have found that both ConvoyWeb and Warsailors have substantial information about ship movements in the Atlantic and Mediterranean but only sketchy information on convoys and ships operating in the Pacific and Indian Oceans.
Good luck and best wishes.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website