Here's what I know about this photo. It's a panoramic photo, most likely a contact print. It measures 3ft by 9in, most likely early 1900's when these cameras were in common usage. The soldiers are all carrying axes and those who aren't in uniform are wearing badges, some with what look to be military medals. There is a train car in the background with "NYC & HR" painted on the side. The family that this came from lived in NY so it makes sense to be taken in NY. Here is the album http://m.imgur.com/a/eRWhn
I believe these are not soldiers, but railway employees. The men in the back appear to be station agents. The men in the front, I suspect, are wearing the company logo -- crossed axes -- on their armband, belt, and hat. This has really caught my interest. I'll be curious what others learn.
Well, the NYC&HR reporting mark on the boxcar is for the New York Central & Hudson River Railroad, in the Vanderbilt era (1867-1914).
The era of the uniforms would put it squarely post Spanish American War but Pre-WW1.
My conjecture is that it is either part of a volunteer corps for a military campaign, such practices weren't uncommon in the Railroad world. Another theory is that this is some crack team of personnel distinguished in their service to the New York Central.
The most reasonable theory is that they may be part of the US Army Corps of Engineers, assisting the NYC in the building of a bridge, tunnel, or clearance of an obstruction due to flooding or other damage.
The photo with all the men in suits and sporting homburg hats look to me like Union organizers.