Nautanki is a traditional, popular form of Drama in India and some other parts of Indian subcontinent. A nautanki is generally full of songs and dances and even dialogs can be in form of songs many times. Hence, the drama form is considered to be a loud one and hence, when someone is called a nautanki, it basically means they're overtly dramatic.
So the phrase 'Nautanki Saala!' would be a slang, calling a person overtly dramatic, in a casual way.