First, the expression uses the word "even", not "ever" as you wrote in your message title. This is a difficult question to answer, because this point of language moves beyond strict rules of grammar and becomes a question of personal style. If I were the editor for that news story, I would tell the writer to change the phrase to one of the following: "Stranger still, the goats' droppings contain..." or "Even stranger, the goats' droppings contain..." To begin a thought where you are introducing a new idea which is stranger than the previous (also strange) thought, you can use the word "even" or "still". It's not very good writing style to use both of them at once. Here are other examples, using similar sentence structure: "Summertime on the coast is hot, but hotter still are the wide expanses of inland desert." Or, with the exact same meaning: "Summertime on the coast is hot, but even hotter are the wide expanses of inland desert." "She was always a shy child, but she became shyer still as she grew up." Or "... she became even shyer..." "Still" and "even" are used in this type of sentence to emphasize the description-word.

In this sentence, "still" just reinforces "even". It is the same thing as "even stranger". You could also say "stranger still", meaning the same thing, but this is not as common in spoken language.

the expression is used like this: here is something strange. even stranger still, [another strange fact/story goes here] basically when you are presenting a statement that is strange, you add "even stranger still" to signify that the story is going to get EVEN MORE strange.

"Even stranger still" just means (in this article): as strange as the goats climbing the tree is in the first place. It's even stranger that the farmers collect their droppings for use in cosmetics. "still" in this sentence is just to emphasize "even more strange than that" Hope that helps!