Back in 2007, I wrote a blog post imagining what Present-Day English would look like if you applied the rules of Old English syntax to it. More than 5 years on, it remains one of the more popular posts here.
That's minor weirdness, though, compared to what Neal Whitman got when he imagined what English would look like if it were an ergative language. And then he upped the ante by extending it to the antipassive.
This is a fun game. We could extend it with pretty much any recherche construction we wanted. What, for example, would English look like if it were highly agglutinative and had only nouns and verbs, like Tamil?