The Celts are so easy. There are just so many to pick from. You could have Scots Galloglass or Redshanks (mercenary axemen), or the Scottish Highlander regiments (muskets or rifles or even infantry, depending on what era you want to focus on - they were renowned in all those periods), or you could have Claymore swordsmen or Welsh longbows or ... yeah, tons of stuff there.
For the Inca, I've always been puzzled why their UU is a mere warrior. Of all the groups encountered in the New World by early explorers, the Inca alone used bronze. They also used long pikes and pole-arms, and were particularly fond of the mace. That's what the Incan warrior in the game actually seems to have, is a mace (the maceman in the game is wielding a flail, not a mace!)
So I'd be thinking a pike, a maceman, or possibly a slinger for the Inca. Chasqui, btw, were just messengers, part of the Incan "postal service", not a military profession.
I think the Iroqouis should have UUs that represent two different eras of Iroqouian warfare. The pre-columbian era, which should probably be some sort of melee troop class, and based on the ball-headed warclub such as depicted here:
http://www.mccord-museum.qc.ca/ObjView/5273.jpg
The other kind should be an Iroqouis shooter/musket. In the wake of European arrival, the Iroquois were able to obtain a great many guns, more so than most other native groups of the northeast. The other groups were mostly allied with the French, and the French wanted to keep guns out of the hands of pagan groups and restricted sales to converted Indians only (and limited those sales, in order to keep them from selling their arms to pagans). The Iroqouis made allies with the Dutch and the English, who just sold them as many guns as they could afford to buy. The result was that the heavily armed Iroqouis, already feared by other native groups of the Northeast, managed to take control of the fur trading routes to the interior and were exerting their military influence as far west as Michigan, controlling the shores of the entire Great Lakes basin from their tiny homeland in upstate New York.