One site has Henry Hodanger listed for the 133rd NY Infantry, Co. K as a Private. Note: Also known as Haudinger. Another site lists him as Henri Hodanager, also in Co. K, 133rd NY INF. Residence not listed; 21 years old. Enlisted on 10/7/1862 at New York City, NY as a Private.
On 10/7/1862 he mustered into "K" Co. NY 133rd Infantry
(date and method of discharge not given)
(Absent in confinement at MO)
He was listed as: Absent POW Ship Island, MS (date not stated)

This regiment was in LA (Port Hudson, New Orleans areas) from Fall of 1862 until July 1864.

Don't know if this is the Henry you are looking for, but it's the only one I could find.

Email me at colleenh@sybercom.net if you need a regimental history for the 133rd.