They are your great nephews and/or great nieces.
Alternately, some people say grand-nephews, grand-nieces.
You are a great-aunt.
their mother and father
She would be the same relation to you as she is to him.
your Neice
We would infact, cll our sisters son your nephew and they would call you either auntie or uncle depending on your sex.
I think it is appropriate to call him your brother.
you call your parents sisters aunty
Potential insanity.
He would be a nephew, unless of course he is a son from a previous marriage, then he would be no relation.
sisters in law
She is your niece.
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