I’m not a current student (graduated in 2011) but I’d love to help you in any way I can. First, I wrote an extensive post on the general atmosphere at GW if you care to read it: http://talk.collegeconfidential.com/george-washington-university/1624808-good-and-bad-of-gwu.html
To your more specific questions:
No, frats don’t dominate. They’re definitely visible, and mostly in good ways. You’ll see plenty of students walking around in their colors, fundraising events, events centered on awareness of a topic, etc. You’ll hear loud parties at some of the houses on campus Thursday-Saturday nights. I’d say that’s about it. It’s pretty easy to not be bothered by Greek life. Also, @NativeFlash is wrong in that fraternities DO have houses on campus. There’s Townhouse Row on 23rd street that has roughly 8 frats and sororities. There are also a few other buildings strewn about campus that house fraternities.
GW is VERY politically active. This is something that you won’t be able to escape if it bothers you. No, it’s not obtrusive or anything, but you’ll see flyers, politically-focused events, and students in classes that love to talk politics. GW is more on the liberal side (naturally) but the College Republicans student account is large and vocal as well.
As far as non-party dorms, that’d be anything that has singles (West Hall on the Mount Vernon campus or Mitchell on Foggy Bottom). As a transfer I think you’re limited to only one dorm but I’m not sure which it is this year. It used to be Lafayette but I think it’s still under construction. Now, with that said, just about any dorm (other than Thurston) can be pretty chill and you won’t be bombarded by parties if you’re not out looking for them. My dorm on the Vern was very quiet, and the next three years at Ivory Tower (now Shenkman Hall) were mostly quiet. There might be parties down the hall but you wouldn’t know it unless you walk by the room and hear music. They typically don’t spill-out into common areas.
So yeah, if you’re not into the parties but still want to have fun other ways don’t worry about it- I was just like you. I went to one or two parties my four years. I’d mostly get together with friends to play video games, watch football, etc. You won’t be out of place if you’re not out all the time.
Feel free to shoot me a message if you have any other questions!