You should probably be using the APIs for each respective Social Media site as opposed to using AJAX to directly try and scrape or make API calls. As an example, the following will retrieve an Activity on the Google+ network that you can use to retrieve engagement counts:
https://developers.google.com/apis-explorer/#p/plus/v1/plus.activities.get?activityId=z120dncann32i3gu222uydqhrp34gx5np&fields=object(plusoners%252Creplies%252Cresharers)&_h=3&
For Google+ you should be using the official Google+ API client, demonstrated on the Google+ JavaScript Quickstart.
As another example, if you are trying to get a count of people who have mentioned a user on Twitter, explore the API for Twitter to find the query you are looking for.
You would then use one of the various JavaScript libraries for Twitter to manage API calls.
For Facebook, you should be using the Facebook JavaScript library.