Even a single faction of the military would totally embarrass all of Middle Earth. Cave Trolls are their most powerful weapons, and the U.S. has sidearms that can blow their heads off in a single shot. Combine that with crowd control full-Auto armor piercing rifles, as well as heavily armored tanks with 40mm shells capable of tearing through and mulling over entire buildings, on a scale including millions of soldiers, weapons, etc?
That's not even taking aerial warfare into account. A single predator drone could probably take on all of Middle Earth, save for a dragon. Their are plenty of aircrafts that could take out a dragon, though.
The only hair in the soup is the undead army- to which the U.S. military would probably resort to trapping on a remote island or something, until they found a way to destroy them. Assuming the ghosts are made of a plasmatic substance, there are plenty of ways to destroy them with science.