What are the origins behind our use of "house is on fire" as opposed to "fire is on the house"?
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On fire is a standard English term meaning burning, or ablaze. It goes back many centuries.
The alternative fire is on the house is simply garbled English. I assume you've just come up with it yourself by playing with word order.
NOTE - Google lists only 8 results for fire is on the house, of which your actual question here comes at the top of the list!
With due deference to RiMMER, I'll just say it's technically feasible for fire is on the house to make sense in certain somewhat surreal contexts. At a subsidised Arsonists' Convention, for example, where the attendees might be expecting fire on the house (i.e. - for free).
The OED says s.v. "on", definition 12.a:
It also says:
The etymological note explains that these words (afire, alive, asleep, and many more) were originally "on fire", "on live", "on sleep" etc. For some reason "on fire" has survived, where many of these phrases continue only in the merged form.
The correct phrase is, "house is on fire," but you also might have been thinking of "it's on the house!" when you wrote "fire on the house."