I am travelling from JFK to KTM via New Delhi, India. My transit time is around 16 hours in New Delhi. Do I have to get transit visa in New Delhi to stay in the airport?
As stated in Timatic, the database used by airlines:
TWOV (Transit Without Visa) Holders of confirmed onward tickets for a max. transit time of 24 hours.
So if the trip is in a single booking, you do not need a visa
US citizen or not, you need Transit Visa if you are not Indian. Although there are visa exceptions for 10 countries Japan, Luxembourg, New Zealand, Cambodia, Singapore, Finland, Laos, Indonesia, Philippines, etc.
The visa service is outsourced to VFS global (UK and RotW) and BLS International (for USA) who deal with multiple countries' visa applications. Here is the link for Indian Visa services in the USA
You probably have to visit this page
One thing is that you have not mentioned in your passport whether or not you hold the dual citizenship (or if you are an Indian-American). In anyway, the links that I provided above should do the job for you.