How to alert users when new content is added via email and/or text message? I have a membership Drupal 7 website and I'd like to automatically alert users via their email address and/or text message to their cell phone when new content is added? I'd also like to give registered users the ability to select/change these communication preferences.

Is there any Drupal way/technique that can provide this functionality?
Have a look at my answer to "How to send an SMS message when a Webform is submitted?", which is a variation of your question here. It describes how you can use the Rules module to get this to work. In your case just use a Rules Event like "after saving new content", and optionally add some appropriate Rules Conditions to better fit your exact needs.