In this case I'm using the word "look" to express two different things. Does it make the text sound unnatural or awkward?
Look how every man in the party are extremely kind with her. That's something that only happens when you have that kind of look.
In this case, no, it seems quite natural to me. After all the entire length of two sentences are between the two uses of "look". But when the repeated words are in closer proximity to one another, it can be come confusing, and recasting the sentence to avoid repetition is often a good idea.
You only have to look, to see her new look is stunning.
Here the reuse of look is far more likely to be confusing. Sometimes this is done intentionally, as a form of wordplay.
There was a young fellow named Hall
Who fell in the spring in the fall.
'twould have been a sad thing
has he died in the spring
but he didn't -- he died in the fall.
Both "spring" and "fall" are used in multiple senses here: body of water, season, and for "fall" accident.
Unrelated to the reuse of "look", the example has an error in agreement.
Look how every man in the party are extremely kind to her.
That should be "every man ... is extremely kind..." because "man" is singular and the form of the verb "to be" must agree. If instead of "every man" the writer had used "all the men" then the form "are" would have been correct.
