He would be his great great great uncle
You are their great aunt/uncle.
Your uncle is your children's great uncle and they are his great nieces and great nephews.
You would be his Great Uncle and he would be your Great Nephew.
You are an aunt or uncle (depending on your sex) to your nephew, and a great aunt or great uncle to his children.
Your uncle-by-marriage's nephews might be you and your siblings. You are your uncle's nephew or niece.They might be the children of your aunt's siblings (your aunt being his wife), in which case they are your cousins.If they are your uncle's nephews by virtue of being children of his siblings, they are no relation to you at all.
Your great grandfather's brother is your great uncle and your grandchild's great-great-great uncle
You are great aunt or great uncle to your niece's daughter and great great aunt or great great uncle to her grandchild.
You are aunt or uncle to your nephew, great aunt or great uncle to your nephew's son, and great great aunt or great great uncle to your nephew's grandchild.
Huey, Dewey, and Louie Duck were the three nephews of Uncle Scrooge.
Your nephews child is your grand nephew/niece.
Your nephew's daughter is your great niece and you are her great Aunt (or Great Uncle).Correction:Your nephew's daughter is your grand niece. You are her grand aunt or grand uncle.
Your great uncle's grandchild is your second cousin.
A nephew has an uncle. The children of the nephew are the uncle's great nieces and great nephews. The uncle is the great uncle of the nephew's children. The children of the uncle are first cousins of the nephew. The nephew's children and the uncle's children are first cousins, once removed, to each other.
They would be your nieces and nephews. You would be their aunt or uncle. Most people wouldn't really worry about the half sister part.
Your relation to your mums uncle is GREAT uncle. You're welcome! 
If your great uncle married into your family some of his nieces and nephews are your aunts or uncles (or your parent) and some are not related to you at all.
The grandchild of your grandmother's first cousin is your third cousin. The grandchild of your grandmother's second cousin is your fourth cousin. The grandchild of your grandmother's third cousin is your fifth cousin.
your brother would be his great uncle
Yes he has several nieces and nephews.
He is their Uncle and they are nieces and nephews.
Your grandchild and the sisters grandchild would be second cousins. The additional generation indicates they would be second cousins once removed.
Your brother's grandchild is your Great Nephew or Great Niece and you are their Great Aunt or Great Uncle.
They are your grand-nephews and grand-nieces.
Your uncle is your daughters great uncle.
Your mother's uncle is your great uncle.