Sit yourself sounds really wrong. Isn't it you seat yourself?
That's translating it very literally. "To sit" is a reflexive verb: at sætte sig. At sætte by itself means "to place". So even though I sætter jer looks like "sit yourself" it's really just "sit"; the reflexive doesn't translate into English.
"Sit yourself down" is perfectly normal, maybe a little colloquial. Without the "down" though it would be odd.
"Seat yourself" is what you'd see on a sign in a restaurant. It's not really what people would say to each other.
Well, I guess Duolingo changed the way it could be translated. I was complaining about the english translation which seems different now.
In the American South "sit yourself anywhere" is not uncommon.
Sit vs. take a sit is both ok, I think, but Duo doesn't even accept 'may' here, which IMHO is better/more presice than 'can'. (I'm sure they're not talking about the ability to sit down anywhere...)
Why is everywhere not accepted??