Your dad's brother is your mom's brother-in-law. He is not related to your mom's sister or her children.
They would be great nieces or great nephews.
If your niece's is by your sister but the brother is by your sisters new husband & another woman there would be no blood relation. If not then he's the nephew
Your brothers granddaughter is your grandniece.
You would be their great Aunt.
Your borther-in-law's children are your nieces and nephews. You are their uncle or aunt, as is your spouse.
She would be the same relation to you as she is to him.
she would be your sister in law
The sister's son would be the nephew of her brother.
Nothing. Your niece in law. Your brother in laws niece.
your second nephew
Your sister would be her great aunt and she would be your sisters great niece.
Your brother's children would be your nieces and nephews.