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Your brother's children would be your nieces and nephews.
Your brother's child's children are your grandnieces or grandnephews.
If it is a boy then it is your nephew. If it is a girl then it is your niece.
Some would call your nephew's children your grand nephews and grand nieces, others would call then your great nephews and great nieces.
Your borther-in-law's children are your nieces and nephews. You are their uncle or aunt, as is your spouse.
Your nephew's children are your great nieces (girls) and great nephews (boys). You are their great uncle or great aunt, depending on your sex.
Your brother's wife's kids would be your nieces or nephews.
Your sister-in-law is either the wife of your brother or the sister of your spouse. The children of your brother's wife are your nieces and nephews, since they are also the children of your brother. In some cases they may be your sister-in-law's children from a previous marriage. Then they are not related to you at all. However, if they are very young, it may be convenient to call them your nieces and nephews anyway. The children of your spouse's sister are always your nieces and nephews.
They would be great nieces or great nephews.
I believe they would be great aunts or great uncles.
You are Great Aunt to your niece's child. The child is your great niece or great nephew.
Your brother's children would be called your nieces or nephews.