How to remove default form tag while rendering output in hook_theme
You're attacking the problem at the wrong level - if you want to modify forms/functionality, the theme layer's too late. Specifically what's happening here is that by default forms have a theme wrapper of theme_form() which adds the form tag. The form template itself should only contain the form's children elements. (And shouldn't contain for example calls to drupal_get_function()).

Here are some ways of adding the forms:


Implement hook_menu_alter() and alter the page callback for the login page to be your own callback. This callback returns the three forms. Don't forget to check for whether the user's logged in like core does.
Create a couple of custom blocks for the other two forms and add them to the login page.
Implement hook_page_build() and add the forms there (quick and dirty!).