Nothing. There is no relationship.
Your wife's nephew is your nephew and his son is your wife's, and your, great nephew.
Your wife's nephew is also your nephew. His daughter is your (and your wife's) great niece.
Your wife's nephew is your nephew, but the English language has no relationship term for your nephew's wife. Just call her "my nephew's wife."
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."
Your wife's nephew would be your son's first cousin.
Your nephew as well...
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.
"My wife's niece or nephew" Hi, in simple words, you could say it's your niece or nephew too; not necessary to be your wife's niece or nephew.
Your wife's brother's son is her nephew and therefore your nephew as long as you remain married to her.
Your nephew's wife is simply your nephew's wife. There is no special term in the English language for that relationship.
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."
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.