Q:

Which Google API can access Hangouts Data?

What Google API would be the easiest to father the following information:

A list of all hangouts currently going on in my Google for Work Organization
People in those Hangouts
Links to join those hangouts.

A:

I think the link below maybe could help.
It provides basic information such as getting the list of participants, getting the URL for the Hangout, and getting the HangoutId.
https://developers.google.com/+/hangouts/api/gapi.hangout#gapi.hangout.getHangoutId

