Harry Belafonte sang a song back in the 1950s: Mama Look A Boo-Boo:
I wonder why nobody don't like me
Or is it the fact that I'm ugly?
I wonder why nobody don't like me
Or is it the fact that I'm ugly?
I leave my whole house and home
My children don't want me no more
Bad talk inside de house dey bring
And when I talk they start to sing:
Mama, look a boo-boo they shout
Their mother tell them shut up your mout'
That is your daddy, oh, no
My daddy can't be ugly so
Shut your mout', Go away
Mama, look at boo-boo dey
Shut your mout', Go away
Mama, look at boo-boo dey
They're all rather familiar and rude expressions. They're all correct (whatever that might mean -- to me it means that people say them, not that I think they're necessarily good or bad) and used. I would rank them all below the threshold of civility. You can probably say something like "And if you want to stay out of trouble, keep your mouth shut unless someone specifically asks for your opinion" without being rude, just frank.
Shut Up
is actually worse then telling them toF**k off
. Mainly because the latter is so commonly heard it has lost all meaning, while the former is rarely used and so therefore sounds really harsh. I can understand the curiosity of wanting to know which one is correct, but please do us a favour and never utter these words.