Your niece's brother is your nephew, not her husband.
The English language has no special term to for the husband of a niece. If you want to refer to him without using his name, the best you can do is "my niece's husband," or "my sister's (or brother's) son-in-law."
Your husband's sister's kids are referred to as your nieces and nephews by marriage. More specifically, you can call them your "nieces" if they are girls and "nephews" if they are boys.
The children of your husband's sister are your nieces or nephews, and you are their aunt, just as he is their uncle.
The children of your husband's siblings are your nieces or nephews. Their children are your great-nieces or great-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.
You call them your nieces, or by their names.
When a couple is married and the wife has nieces who are daughters of her brothers or sisters, those nieces are also the nieces of her husband. So your great grandmother's sister's husband could have great nieces who are related to you and also great nieces who are not related to you.Note that your great grandmother's sister is your great great aunt.The great nieces who are related to you are the grandchildren of the siblings of your great great aunt.Those could be your:parentauntfirst cousins, once removedsecond cousins, once removed
You are not related to your niece's husband, although some would call him your nephew by marriage. But that is a relatively recent construction and not used by many. You could also call him your brother's (or sister's) son-in-law.
You would refer to them as your nieces, thought they are formally your wife's nieces. And they would normally call you uncle.
Even thought you not related in genealogy sense you are related by marriage and you can say they are newphew and nieces in law.
They are your nieces and nephews.
He is their Uncle and they are nieces and nephews.
You can refer to your sister's children as your nieces and nephews. If your sister has daughters, they are your nieces, and if she has sons, they are your nephews. Collectively, you can call them your nieces and nephews or simply refer to them as your sister's kids.