I also descend from Hillary Stoker. I have a good deal of Stoker info on my ancestry.com tree, including photos, although none of Edward.
Edward appears with his family on the 1850 Murray County, Ga. census - he is 22 at the time and was born in Tennessee
There is an Edward "Staker" (corrected recently as Stoker on the census as appearing on ancestry.com) on the 1860 census, Catoosa County, Ga.
The ancestry.com Civil War record says he resided in Whitfield County at the time of enlistment or that could be the muster site (I have not looked at the 36th Ga. info in a while) Some of the other posters here would have correct information on where the regiment was mustered in.
I have visited the grave of his brother, Henry Clay Stoker. It is marked but doesn't have a Confederate stone.
The Stoker brothers appear to be bounty soldiers, joining in spring of 1862 after the conscription laws were being enforced.
Again, it has been some time since I looked at their records but I believe there is no record of several of them after Vicksburg.
You may e mail me at dekalbleaves@usa.com if you wish. I can check on the items above for clarification.
G. Patton