you would be the child's great aunty or uncle
Therefore, they would be your great niece or nephew.
Nephews and nieces
2nd uncle I believe
3rd cousin
You are their great aunt/uncle.
Your borther-in-law's children are your nieces and nephews. You are their uncle or aunt, as is your spouse.
Your uncle-by-marriage's nephews might be you and your siblings. You are your uncle's nephew or niece.They might be the children of your aunt's siblings (your aunt being his wife), in which case they are your cousins.If they are your uncle's nephews by virtue of being children of his siblings, they are no relation to you at all.
He would be his great great great uncle
You would be his Great Uncle and he would be your Great Nephew.
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 nephew's children are your great nephews and great nieces (or grand nephews and grand nieces).
Second cousins once removed.