In this usage, "off" involves departing. If you say "Off they went" maybe you want to emphasize that they departed in a dramatic fashion or for some important purpose. You wouldn't say it for some routine trip, for instance you wouldn't say "Off they went to the store" (unless you want to be funny), but the narrator of a documentary film about young soldiers departing to fight a war might say "Off they went, and many never came back." If you say to someone, "Off you go!", then you are usually dismissing that person or maybe sending them on some mission, and encouraging them to leave quickly. The verb is always "go" or sometimes a similar verb like "march", as in your example. Note that you can't say "go off" instead. Although that is a valid phrasal verb, it has a different meaning. "The bomb went off" = The bomb exploded. Sometimes "off" is used without a verb. "I'm off to work" = I am leaving now to go to my job. And if you watch a horse race like the Kentucky Derby, then at the moment when the race begins and the horses start running, the announcer usually says, "And they're off!"

Off is an adverb most commenly used as a command for discontinuing something. Switch off the light. The car was switched off. But it can also be used when someone is leaving He walked off They ran off in a rush It can also be used to describe food that is no longer edible The apple tasted off So when thinking of the word off just remember it's to discontinue Stopping ending terminating etc..