My parents moved to NYC from Guyana in 1978 when my older brothers were 4 & 5. My father got US citizenship long before my brothers turned 18 and my mother got citizenship long after. I'm trying to figure out whether they are citizens since my father naturalized before they reach 18 years of age. Any help is appreciated. Thank you.

Can anyone please help me?

No they are not. If your father got his citizenship it is his job to file for your brothers, unless your brothers where born in the US, they are not citizens if no kind of paper work was filed for them.