Greatly influenced by the Protestant missionary Samuel Kirkland, the Oneida
was the only one of the five-nation Iroquois League who sided with the colonists during the American Revolution.
Option Elimination - In this case, "the Oneida" refers to the tribe (or one of 5 nations in the Iroquois league) and is singular. One more example: The Oneida is a Native American tribe in New York. BUT "the Oneida" can be plural as well if it refers to the group's individual members. E.g., The Oneida are known for their long-standing cultures and traditions. So, if you see "The Oneida," it's not always singular. We need to look at the context.
One more point aligned with this.
When "The Oneida" refers to a group or a tribe - we can't use "who" as "who" has to be used with living beings. E.g., The Oneida tribe, which has a rich cultural heritage, continues to celebrate its traditions. BUT
When "The Oneida" refers to individual group members, "who" is okay. E.g., The Oneida, who have a rich cultural heritage, continue to celebrate their traditions.
So, decide based on the context of the sentence. In this GMAT sentence, "The Oneida" refers to the tribe (as we talk about one amongst the five-nation Iroquois League), so "who" is not ok.
Moreover, "influenced" is an "ed" verbal modifying the subject "The Oneida."
(A) was the only one of the five-nation Iroquois League who sided - "who" wrong.
(B) was alone of the five-nation Iroquois League when they sided - "they"? Wrong.
(C) alone among the five-nation Iroquois League sided - ok.
(D) were the only ones out of the five nations of Iroquois League in siding - "were"? Wrong