Ms. Goodwin,
Do you have an middle initial?
Where are they buried at?
Do you know where they lived at (county and state) during the 1860 Federal Census?
Below are the only soldiers by these names that show up in the National Park Services Civil War Soldier's and Sailor's System.
Private Oscar N. Goodwin Company K, 2nd Massachusetts Cavalry
Private Henderson Goodwin Company C 73rd Illnois Infantry
There are a number of possible soldiers with the initial "O" or "H" but without a middle initial or knowing the location of burial or where (county and state) they lived in the 1860 Federal Census it will be difficult to link them to a regiment.
I hope this helps.
Respectfully,
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment
http://39thgavolinfrgt.homestead.com/39thHomepage.html