How can I display a login and registration form, with an extra field on registration, and hybridauth in a modal?
Yes, this has a common solution with preexisting modules. Here's the summary with your 3 requirements:


Forcing capture of telephone on registration: 


After enabling the Telephone module, you can add a phone field on a user entity (http://example.com/admin/config/people/accounts/fields). When you create the field, make sure the Display on user registration form &amp; Required field checkboxes are ticked to enforce user submission of this data on registration &amp; edit.

Hybridauth Social Login: 


After enabling the module, and installing the libraries to the sites/all/libraries directory, configure each social network and set your other login options accordingly.

Modal Popup: 


The Modal Forms module enables popup modals for the both the user/login &amp; user/register paths. The popup presents the same login form as you see in Drupal so it will contain the HybridAuth login elements as well. The module lets you configure modal popups on a per-page basis so you can choose the pages where you want login/registration presented as modal form.