The uncle's nephew would be first cousins with the uncle's children. So the nephew would be a first cousin twice removed with the great granddaughter.
Your great aunt's son is a first cousin to one of your parents, and is your "first cousin once removed."
The wife of someone who is a great uncle is the great aunt of her husband's great nephew.
The English language does not contain a specific term to describe a relationship between you and your nephew's wife. The culture does not consider her to be related to you. Most aunts and uncles would merely call her "my nephew's wife."
It could be your son. It could be your nephew as well. It could be no relationship to you at all. The question is do you share a common ancestor? If you do not have a common ancestor, you are not related.
Your wife's nephew is your nephew and his son is your wife's, and your, great nephew.
You are not related to your uncles wife sister. However some may think an aunt
There is no specific term in the English language to describe a relationship between you and your nephew's wife. Most people would say you are not related. If you must use some phrase, the phrase "my nephew's wife" is probably the clearest and most direct.
Your wife's nephew is also your nephew. His daughter is your (and your wife's) great niece.
Your great uncle's wife is your great aunt. Her nephew is either the son of one of her siblings, in which case he is not related to you, or he is the son of one of your great uncle's siblings. He could then be your father or one of your parent's brothers.
The English language has no special name for a nephew's wife and does not consider you to be related to you. You would simply call her "my nephew's wife."
The nephew of a wife and the nephew of her husband are not considered to be related to each other. However, both are nephews of the wife and the husband, and the wife and husband are aunt and uncle to both nephews.
If your great uncle is the brother of one of your grandparents, his wife is your great aunt but their nephews and nieces onher side are not related to you. Those nieces and nephews (and their children the great nieces and great nephews) have no ancestor who is also one of yourancestors.
In the English language based culture, your wife's sister's son's wife is not related to you. She would be called your nephew's wife.
You are not related to that person.