Most of the "private games" are our clan events, and are open to all members. The passwords are listed in the scrims forums, along with time and the server that it will be held on: http://www.edgegamers.org/forums/showthread.php?t=56306
The only time you couldn't join one of these is if it is a ranked scrim, and your rank isn't playing. For example you, as an e, wouldn't be able to join the eG vs. eGO scrim. All of our other events are open to all clan members on a first come, first served basis.
Come early, they tend to fill up fast, and be sure to stick around a bit after to help repopulate the server!
Yes, like the above posters have said, they're usually just meetings to discuss important TF2/eGO related topics or just eGO only events, such as the listed above.