Corrected sentence: You can tell an oryx by its long, sharp horns.
Why: The words "long" and "sharp" are two adjectives describing the horns. When two adjectives of the same kind describe a noun, put a comma between them: "long, sharp horns." Also, "an oryx" is correct because the word "oryx" starts with an vowel sound (it sounds like "or-"), so we use "an."
Another way to say it: You can recognize an oryx by its long, sharp horns.