More or less as in the film BUT they were eager to leave the Earth, and they only needed to heed their oath. They do so in a side battle (near Osgiliath IIRC) and, immediately, Aragorn sets them free.

But they are not “an army at the ser ice of Aragorn”. They just want to be liberated and to do so, they fulfill the promise they broke. They are not obligated to more (and Aragorn has no power to keep them “here”), much less to make them obey him.

In the original the army of the dead was used to capture the ships, and grab the army under a Prince in southern Gondor, (I think it was Imiril) and bring his army up from Osgiliath, to surround the armies of darkness on 3 sides, who then broke and ran.

Were they a tide of untouchable murder ghosts though? Or were they more of a conventional zombie force that could be killed?

They cannot be killed but their aim is to abandon Earth, and they only need Aragorn to liberate them after they have fulfilled their oath. Not that Aragorn has true power over them. He has only the power to set them free, and they obey because that is the way to freedom.