Your nephew's child is your great niece (if a girl) or your great nephew (if a boy).
Your brother's child's children are your grandnieces or grandnephews.
Your nephew's wife is your Niece-in-Law, whether she is caring for a child from a previous marriage or not. Few people would care to be that precise, however, so most will probably just call her your Niece.
Nephews
your nephews
Some would call your nephew's children your grand nephews and grand nieces, others would call then your great nephews and great nieces.
Your nephew's children are your great nephews and great nieces (or grand nephews and grand nieces).
your niece's or nephews
If it is a boy then it is your nephew. If it is a girl then it is your niece.
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.
The children of your husband's siblings are your nieces or nephews. Their children are your great-nieces or great-nephews.
Second cousins.