periamma
You would call your father's sister "பெரிய அந்தை" (periya anthai) in Tamil.
In Tamil, elder sister is called "அக்கா" (Akka).
akka .. for elder thangai for younger
சகோதரி, தங்கை, அக்காள் (sagothari, thangai, akkal) sister, younger-sister, elder-sister.
cousin
Husband of your sister is called 'aliyan' in Malayalam.
Mom
In Tamil, you would call your father's sister's daughter "சகோதரி" (sahothari).
Sister's husband is called Athimber (Brahmin way of Tamil) or Maamaa
You should call him "sagalai"
In Hindi, you would call your mother's sister "mausi" or "masi".
Suck me willy an call me Joseph