I have the following packages and their dependencies installed in my WebAPI project:
Ninject.Web.WebApi Ninject.Web.WebApi.OwinHost
Ninject.Web.WebApi
Ninject.Web.WebApi.OwinHost
Did you modify your OWIN Startup class to call app.UseNinjectWebApi and app.UseNinjectMiddleware rather than calling app.UseWebApi?
Startup
app.UseNinjectWebApi
app.UseNinjectMiddleware
app.UseWebApi
Startup.cs in the Ninject Web API samples does this...