He would be his great great great uncle
Your brother's wife is your sister-in-law and her grandchild is also your brother's grandchild - and thus your great niece or great nephew. Your spouse's sister is also your sister-in-law. Her child are your spouse's nieces and nephews and her grandchildren are your spouse's great nieces and gereat nephews. By custom, they are yours as well, however in terms of actual genetic relationship there is none and you might call them "my sister-in-law's grandchild" or "my spouse's great niece or great nephew.".
Your grandchild and your sister's grandchild are second cousins.
Your grandchild and your brother's grandchild are second cousins.
Your first cousin's grandchild and your grandchild are third cousins.
Biologically, the grandchild is a step-grandchild to the grandparent that had no children. In matters of the heart, however, the grandchild is whatever the grandparent feels it is.
The plural of grandchild is grandchildren.
Santa's grandchild is Kellen Welch.
You call them your nephews.