According to the National Park Service Soldiers & Sailors database the four John O'Neils served in the following regiments:

The 1st Vermont Infantry organized at Rutland and mustered in for 3 months May 9, 1861.

The 3d Vermont Infantry organized at St. Johnsbury and mustered in July 16, 1861.

The 10th Vermont Infantry organized at Brattleboro and mustered in September 1, 1862.

The 17th Vermont Infantry, organized in 1864.

If you can determine which is your John, you can order his Compiled Military Service Record through this message board.