Say it to most Americans I know and they think you're moving a residential structure on a flatbed truck from one lot to another.
When I was little we "moved house" from the farm to the village. We spoke in some vaguely old British ways, apparently leftover from my ancestors. The area where I lived then, at the farm, was in northern New York, where people have a dialect all their own anyway. Cows are "caowz," for example. Not quite two syllables, but slightly more than one.
There are other examples, but this particular expression strikes me every now and then. To my ear, after all these years among people who don't instantly understand, it sounds archaic, charming.