"The house has many stories."
Translation:Huset har mange etasjer.
Yes, that would be correct when "stories" is the plural of the English noun "storey". Another possible translation is "huset har mange historier", if "stories" is the plural of the noun "story".
EDIT: I just discovered that in American English, "story" is used instead of "storey" also when it means "level" or "floor"
Okay, so I looked it up out of curiosity - apparently the US drop the e in storey, and the plural is stories?! This confused the crap out of me, as the British English is storey/storeys. I interpreted the sentence as some sort of "if these walls could talk" thing. Usually I concede that the American version of English is easier, but I think we win this round when it comes to clarity ; )
As an American, this is the first I've heard of storey (and the first I've heard anyone speak positively of American English vs British English). Must be strange from your perspective, but having 1 word with multiple meanings isn't so bad. As a poet, I find it rather useful. So if the house has many stories, I just told the reader a lot more than I could have with a less versatile word. But for everyone who isn't writing, yeah, clarity is probably more important.