What's the point of the strange way of speaking in the film? (sp)

I am wondering exactly the same.

its one big allegory

Just part of Lanthimos's Brechtian alienation strategy, which he employed also in "Dogtooth" and, as you mention, "The Lobster". It definitely seems less motivated in this case, though.

Yeah . . . I'm in the middle of watching this right now and was wondering the same thing. It's also strange how none of the characters seem "real." I'm not sure what they're going for, but I'm still interested.

In "The Lobster," I didn't take issue w/their speech patterns b/c of the nature of the world in which they were living. It made sense for me there. Here, we're supposed to believe this is the actual world, but all these characters are straight up weird.

I kind of like the weirdness of the language, but I did wonder if it might simply be that the filmmaker is not a native English speaker? Can anyone who is a native speaker of Greek tell us whether his Greek-language films use strange, stilted speech as well?

They are pod people. =P

It does make them feel cold and detached... Which makes it weird when they do show emotion... crying, hitting, yelling etc.

I have no idea why the director chooses this way of speaking... but I feel it would have been more emotional if the characters would have talked like real people...

I think it's just used for dramatic effect. In The Lobster, it's funny. In The Killing of a Sacred Deer, it's terrifying.