PHP: what is the fastest way to implement a traditional registration & social (twitter, fb etc) registration?

probably Auth0; the free account limits are pretty good.

Meanwhile went with @denemio's suggestion - https://github.com/gigablah/silex-oauth

in django .. django-registration

PHP: what is the fastest way to implement a traditional / WIP

I would say Laravel.

It's only one command to create your whole authentication system and you can add social oAuth very easy with laravel.com/docs/5.5/socialite