Luckily, The GW Hatchet has an extensive list of student organizations on Twitter. A quick scan of the list shows that the most active of GWU organizations on Twitter and those with the most followers seem to be The GW College Democrats, The GW College Republicans, and the Program Board. Each account has in the neighborhood of 500-600 followers, and gains about 5 followers per week, according to Twitter statistics analytics website, Twitter Counter.
As for how the organizations are using Twitter, they all seem to use the site primarily to get the word out about events to their memberships:
The more ideological and political organizations tweet news articles they think their memberships will find interesting:
The other most common use of Twitter is for PR and publicity reasons. The organizations will often re-tweet articles by campus media covering their events:
So far, student organizations aren't fully utilizing the social media tool. Even the three largest organizations only have about 600 followers each. That amounts to a very small fraction of the student body. For Twitter to be a legitimate and proven promotional tool, organizations have to get more followers, tweet more often, and continue to provide content and information their memberships find useful.