The traditional terms were "great-nephew" and "great-niece" but grandnephew and grandniece are identically defined: the children of a niece or nephew, i.e. grandchildren of a brother or sister. The terms may have first been used circa 1804.
Well, I really haven't had the opportunity to meet them and make any sort of opinion...
If I were you, Grand-uncle, I would call them my grand-nieces and grand-nephews.
Your brother's children would be called your nieces or nephews.
Your brother's children would be called your nieces or nephews.
Children of your siblings are nieces and nephews. Children of your spouse's siblings are still called nieces and nephews, but you are not related to them by blood.
Your brother's child's children are your grandnieces or grandnephews.
Some would call your nephew's children your grand nephews and grand nieces, others would call then your great nephews and great nieces.
If it is a boy then it is your nephew. If it is a girl then it is your niece.
Your borther-in-law's children are your nieces and nephews. You are their uncle or aunt, as is your spouse.
Your brother's children would be your nieces and nephews.
Your brother's wife's kids would be your nieces or nephews.
Most people just say in-laws. Technically, I think they would be nieces and nephews, but only by marriage.
Nieces and nephews are the children of your siblings.
Nephews and/or Nieces