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[LOTR] How does an army of men or elves fight a Balrog?

In the first age, Balrogs fought for Morgoth. How did the elves deal with them if they encountered them in battle?
gpt
First things first: Forget the image you have of the Balrog from the film.

Second: You must understand that Tolkien's writings evolved over the years, and while some things were updated by him in later times, others were not.  
This is relevant with Balrogs because, in the first writings of the Silmarillion and similar stories, there were many, many Balrogs, whereas by the time the Lord of the Rings was written, there were only very few (3 or at most 7) to ever exist in the universe's history.  

Appropriately, the "earlier" (speaking conceptually, not in in-universe history) Balrogs are much less powerful than the ones of the later writings. So since you're asking about the first age, I'll be answering under the assumption of the Balrogs being one of these ("early") ones.

So, how do the elves fight and kill them? With swords, mostly. Glorfindel and Ecthelion take out a Balrog by themselves:

>Ecthelion duelled Gothmog in the battle over Gondolin. During the duel, Ecthelion lost his sword. Gothmog then was about to deliver the final blow when Ecthelion jumped and drove the spike of his helmet into Gothmog's body. Gothmog then lost his balance and he, along with Ecthelion, fell into the Fountain of the King. Gothmog and Ecthelion both drowned.   

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>Glorfindel stabbed it in the belly, but as the balrog fell it reached out and grabbed his long golden hair, pulling him back down over the edge of the cliff. 

Again, it is important to note that this kind of Balrog is not the same thing as what Gandalf fought.

Now, Glorfindel and Ecthelion are exceptional individuals, so one cannot assume that just any elf can go one-to-one with a Balrog and win. However, it's probably fair to say that a group of elven warriors could feasibly take on and chase off, if not defeat, one of these Balrogs.

As to what the case would have been had Tolkien gotten around to rewriting these earlier encounters with Balrogs and making them fitting, we can't really say.