http://plus.google.com/hangouts/_
That will redirect you to a new hangout URL, and (in my experience) you can just copy/paste the new URL to other folks. To use it, they'll need to be logged into a G+ account, but it doesn't matter which one.
I find the screen sharing feature in Skype to be poor quality. We tend to use Skype for calls, and then join.me for screen sharing.
We sometimes have call quality problems on Skype too. We also switch to hangouts for this reason, and we are often surprised how good the call quality, video quality and screen share quality is on hangouts.
Only problem is that nobody can figure out how to login or start a hangout. The interface is damn awful. They need a simple app like Skype's that installs like Chrome does, and give me history for gods sake. How hard is that to deliver?
One of the reasons I shy away from hangouts, is that I use Skype to backfill my timesheet. I can see exactly what calls, video calls, chats I made going back to 2006 on Skype's history. Admittedly so can the NSA, but still, the feature is awesome from a work perspective.
I bought an iPad to my mom for Christmas and facetime with them now. It's the best I've found - even easier for them to use than Skype. They call me, I call them, there no confusion anymore.
No idea about the group chat, but I will agree on Skype working really badly (despite their 10+ years of experience) compared to newer solutions as hangout and facetime.
Are you telling me that you experience the opposite? If so, that's very odd.