Your grandchildren and your great niece are second cousins to each other.
Your niece is the first cousin of your children and the first cousin, once removed, of your grandchildren.
You are related "by blood" to anyone who is descended from someone you are also descended from. That includes your great grandfather and great grandmother and all their children, grandchildren and great grandchildren.
The son of your great niece is your great great nephew.
Your niece's son is your great nephew. You are his great aunt or great uncle.
You are your neice's aunt, your neice's children's great aunt, and your neice's grandchildren's great great aunt
Your niece's husband's daughter is also your niece's daughter and therefore she is your great niece. You are her great aunt or great uncle, depending on your sex. If your niece's husband's daughter is from a previous marriage, and so not also your niece's daughter, you are not related to her. Of course, if your niece adopts her, then she is your adopted great niece. If your niece married her husband while his daughter was very young and everyone has been treating her as your niece's daughter, then you can call her your great niece if you want, but that does not change the fact that you have no common ancestors and therefore are not related to each other.
Your grandchildren and your niece are first cousins, once removed, to each other.
Great nephew. Your children are the first cousins of your niece and your children would be first cousins once removed. Your grandchildren and your niece's child would be second cousins.
maybe
your grand niece or nephew in-law (-Kasadie)
Great-great-great Aunt/Uncle. You basically aren't listed as anything else after the first 'great' to that line.
Your grandson and your great great niece are second cousins, once removed, to each other