"Where are the eggs?"
It sounds as strange as "Eggs where?" in English. You put an object first and then the verb. I guess "Яйца, где они?" would be only used in emotional speech. That's my thought. While living in a country where literally almost all older people are able to speak Russian, I've never heard a phrase "object+verb" in a casual language.
Why does it say I'm incorrect when I translated the sentence this way: "где этих яйца?"