I found James W. Godbey or Godby's record online on the MO Sec'y of State's website at http://www.sos.mo.gov/archives/soldiers and his record from the Missouri State Archives there seems to give his total service (and that of several other men with that surname) as part of Company F, 63rd Enrolled Missouri Militia Regiment. Since this is a "grassroots" militia unit and I don't think it was federalized, you will probably NOT find this man's military service record also at the National Archvives and Records Administration in Washington, D. C. That is, if Godbey performed other Civil War service, I don't see evidence of it on the online MO State Archives site.
The record states that Sergeant James W. Godbey or Godby (there are two records) was enrolled into Captain Wheeling's Company F of this regiment at Rolla on September 10 1864 and that he served 60 days active service at Cuba, Crawford County, Missouri between September 10 and November 10, 1864 (during Price's great Missouri raid). I would guess that his duties at Cuba probably involved guarding the railroad facilites there against guerrilla sabotage.
I hope that helps.