To start, you're likely going to need to leverage a few different APIs. Since I cannot add a comment to ask questions, here's a recommended reading list based on my recent work with the Plus & Hangouts APIs:
Google Plus - https://developers.google.com/+/api/latest/people/list - Collect a list of people in your circles. This will not tell you who's online or offline. May be optional (see #2). Unfortunately, this call is not available yet in the PHP Client Library, so I created one for my personal project and am waiting on some vetting to submit it back to the Google project. If you're interested, I'd be happy to share.
Google Talk - https://developers.google.com/talk/ - Use that query the Talk service to see who's online and/or offline.
Starting a Hangout - Seems this discussion @ the developer group is similar to your question and can best point you in a good starting direction. https://groups.google.com/forum/#!topic/google-plus-developers/r_f7iweZ7c8
Hope that helps & curious to hear how it goes!