Shut your mouth

I’m confused regarding these expressions:

Shut up

Shut your mouth

Shut your mouth up

Shut up your mouth

After some research, I’ve come to believe they are all correct except “Shut up your mouth”. Am I right? Even if not correct, is “Shut up your mouth” still commonly used? Are all four expressions common to some extent?

I know they are all rude, but are they equally rude or they could be ranked by level of rudeness?

The first two are used and are normally rude, and the third might be heard occasionally. The fourth is unlikely, but there was once a popular song in the UK called ‘Shaddap You Face’.

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.