With Facebook, you can do this:
http://api.facebook.com/method/fql.query?format=json&query=SELECT total_count FROM link_stat WHERE url="http://stackoverflow.com OR url="http://stackexchange.com" OR url="http://example.com"
However, with Twitter, Google, and LinkedIn, I can only figure out how to get information about one URL at a time. Here are the URLs (took me a while to find):
http://urls.api.twitter.com/1/urls/count.json?url=http://example.com
https://clients6.google.com/rpc (Google uses a POST request)
http://www.linkedin.com/cws/share-count?url=http://example.com
How can I get information about multiple URLs in one request from Twitter, Google+, and LinkedIn
One HTTP request is directed at only 1 url. How else would an HTTP request get routed to the correct place if it couldn’t figure out the IP address of where to send the request?
You do have a solution. Write a web service on your server such as
http://www.example.com/ajax/GetAllAtOnce.asmx. In your server-side code, you create four web requests, gather back the information and send it back to the client.