For clarity, lets call your great great grandfather's niece "the niece".
The relationship sequence:
(1) The niece is the daughter of your great great grandfather's sibling
(2) The niece is a 1st cousin of one of your great grandparents
(3) The niece is a 1st cousin once removed of one of your grandparents
(4) The niece is a 1st cousin twice removed of one of your parents
(5) The niece is your 1st cousin three times removed
Your father's great niece is your first cousin once removed.
Your grandmother's great nieces are your second cousins.
Great-niece.
They would be great nieces or great nephews.
They are your great nephews and/or great nieces. Alternately, some people say grand-nephews, grand-nieces.
Your borther-in-law's children are your nieces and nephews. You are their uncle or aunt, as is your spouse.
You are her great-great Aunt (or great grand Aunt, depending upon your preferred nomenclature). She is your great great niece.
Sisters, mother, aunts, grandmothers, nieces, cousins, etc.
Your aunt's grandchildren would be your first cousins once removed, as the your aunt's children are your first cousins.
Second Cousin
Your niece's son's son is her grandson. He is your great great nephew and you are his great great aunt or great great uncle, depending on your gender.
Your niece's son is your grand-nephew. You are the child's grand aunt, or grand uncle (whichever applies).
Nephews and nieces
your 2nd niece...!