Here are countries Nigerians can travel Visa-Free with a US visa, UK visa, Schengen Visa.
For visa-free/visa on arrival countries:
US Visa Interview Questions And Answers:
Countries who waive visa requirements for citizens of countries who would ordinarily require a visa – if they have a US/UK or Schengen visa, usually provide the terms and conditions. Such terms may include certain visa categories, the maximum duration of stay, or the requirement that the visa must be valid for a certain period and/or the visa must be used at least once.
These terms are usually straightforward and you should always read about them on the official websites of the applicable countries.
Some people obtain at least one of these visas and do not get to maximize their visas. That is changing now because these countries that you can visit with a Nigerian Passport if you have a US/UK or Schengen visa.
Because policy change often, always reconfirm the updated policy on the official website of the applicable country before you travel.