in others' eyes

"I have seen a trace of strain

In other's eyes, not spoken"

That's a typical mistake, even from a native speaker.

In the eyes of others when used as a possessive becomes: in others' eyes.

As for "a trace of strain", that can apply to a plural noun after it.

• There was a trace of sadness in the eyes of the people at the funeral.

• I have seen a Christmas tree in others' gardens.

That means each of the others have a Christmas tree in their garden.

• There was a large, red ball left at all our houses by the rich man.

Not really.

In the Christmas tree example, I'd prefer the plural since there are really multiple trees. (Although note that Christmas trees are not normally in gardens, the point of them is that they are brought inside). I would accept the singular, to indicate "one tree per garden". This is the common problem of plural possession.

However The "trace of strain" is a metaphor; it's figurative language; he isn't talking about a real "stain". The "strain" is the difficulties of modern life and love, or something. It's probably meant to be universal comment on the human condition, and the singular seems very appropriate here.

You're probably right about "others'" Apostrophes are a common mistake by native speakers.