I'm Nigerian, passing through JFK on Delta Air on my way to St. Kitts and Nevis on tourist visa on arrival policy. I want to know if it is possible without a transit visa.
Unfortunately, you need a visa. It could be a transit visa (C) or a visitor visa (B). All passengers in the US, including transit passengers, must clear immigration controls, and the US did away with its "transit without visa" facility many years ago.