I've never heard that in my life. Usually we'd simply say the day after tomorrow or aftertomorrow for short.

As an American, I've never seen or heard "overmorrow" in my life; we always say "the day after tomorrow" (although "übermorgen" is perfectly good in High German). Another alleged English word that we don't use very often (at least in America) is "forenoon", although most native speakers should recognize it (unlike "overmorrow").

It's not natural. Nobody actually uses it. That day is referred to as the day after tomorrow. Overmorrow is just a nice word that dictionary nerds know 🙂