You ask an excellent question about three prepositions of agency -- (1) through, (2) with, and (3) by -- used with the word eyes. Eyes have two capacities: (A) they are one way the world communicates to us (as the organs of sight) and (B) they are one way we communicate to the world. Sense A is seeing; sense B is looking at.
For sense B, we have the saying the eyes are the windows to the soul, i.e., our eyes reveal to others who we truly are. We say, "Her eyes flashed with anger" to indicate that somebody looks angry. And in your examples, two people send wordless messages to each other by a glance, a wink, or some other action using their eyes. All three prepositions are used in both senses.
(A) From Their Eyes Meeting the World: the drawings and
paintings of children by Robert Coles and Margaret Sartor
She told us that you have to think of other people, and not just yourself, and try to see yourself through their eyes, and not
just your own — but it's hard.
This is a common metaphorical expression for using another's eyes to mean to see what they see.
(B) From Return Trip Tango and Other Stories from Abroad by F MacShane
and M Carlson (1992)
It's through their eyes that I understand that animals are something else.
This is the other sense. The narrator is looking at animals' eyes for her understanding.
(A)With Blood in their Eyes by S G Lawrence (1961):
They'd simply followed his every footstep with their eyes,....
That is, they saw the footsteps.
(B) From Secrets from the Casting Couch: On Camera Strategies for
Actors from a Casting Director by Nancy Bishop (2009):
I believe that this was in part because they had so much practice with communicating with their eyes.
That is, they had other people looking at their eyes.
(A) From Intellectual Repository and New Jerusalem Magazine (Vol 5, 1839)
But spirits may be made sensible of the existence of the natural world by communication with the spirits of men while in the body, so
as to see, as it were, by their eyes,
That is, inhabitants of the spiritual world may become aware of the
natural world by seeing things by using the eyes of humans.
(B) Holding the Dream by Nora Roberts (1997):
You can tell by their eyes. You can tell if you look in their eyes.
And here again, the other sense, of people looking at eyes.
Prepositions often have numerous shades of meaning and idiomatic usages, but in this context, they all mean the same thing, whether it's taking signals in (i.e, seeing) or by sending signals out.
As a side note, eyes in your examples needs a preceding determinative, probably their.