There are a range of possibilities, depending on the exact relationship. If the nephew is the son of one of your cousins (i.e., they are the child of one of his brothers or sisters) they would be a first cousin twice removed. If they are the child of one of the spouses' brother's or sister's spouses, there is no relationship, though most families would probably refer to them as a distant cousin.
Your father's great nephew is the son of your father's niece or nephew. Your father's nieces and nephews are your first cousins. Their children are your father's great nieces and great nephews, and are your first cousins, once removed.
Your son and your niece are first cousins. Her daughter and your son are first cousins, once removed.
Your son and your nephew are first cousins to each other. Your son's daughter and your nephew are first cousins once removed.
Yes, of course your son and your great niece are related. They are first cousins, once removed, to each other. (Your great niece's parent, your niece or nephew, and your son are first cousins to each other.)
Second cousins once removed.
They are out of synch by a generation. They would be first cousins once removed.
The children of your uncle are your first cousins. The children of your first cousins are you first cousins once removed. Thus the grandchildren of your uncle are first cousins once removed. The related link I will make below explains how all this works.
Your first cousin and your son are first cousins, once removed, to each other.
The first cousin of your dad's first cousin is also your your dad's first cousin or is not related to him or to you. The children of two first cousins are second cousins to each other. So the son of the first cousin of your dad's first cousin is either your second cousin, or is not related to you at all.
Sam and his mother's sister's son are first cousins, just as you and Sam are first cousins. But you are not related to Sam's mother's sister's son.
Your sister's daughter and your son are first cousins to each other. Your sister's daughter and your son's daughter are first cousins, once removed to each other. Your son's daughter and your sister's granddaughter are second cousins to each other.
Your son and your niece are first cousins to each other. Your son and your niece's son are first cousins, once removed.