a77 , nex 7, or panasonic gf3c

If you are just starting out... the Nex-7 may be too complicated.  Most of the features are hidden inside menus, the top knobs are counter-intuitive for someone only just scratching the surface of understanding Aperture, and what the heck an ISO is.

Having a full on DSLR, means its bigger, heavier, more full time knobs and switches, and over all noob-friendly features.

Both cameras have the same sensor, and processor... so comparing them on image quality is moot.

The real BIG selling point, is the lenses.  The Sony Alpha lenses are faster for auto-focus, much less expensive, and vary a lot in terms of focal ranges.

The Nex-7, has the ability to use adapters to work with pretty much EVERY lens ever made, for any camera, though Auto Focus is lost on any lenses besides the Sony Alpha lenses (with the translucent mirror adapter), and Canon's EF or EFS lenses, (using a special adapter from the RJPHOTO website). 

I went with the NEX, because I have experience with the NEX, and all of my lenses are Manual Focus Legacy lenses from 40'-80's... aside from one Alpha DT 1.8/50 SAM.

I would definitely recommend the Sony SLT A57, because it's ability to capture photos in low light is amazing. Image stabilization is built inside the camera so you don't have to worry about changing lenses. Also, it can takes up to  12fps in continuous mode, which is magnificent thanks to the Single Lens Translucent that Sony developed. 

One thing is that it's not a DSLR but I would highly suggest in this camera. The price is very decent compare to others DSLR such as Rebel T3i (Canon), D7000 D90 (Nikon) or anything listed above from Sony so that you can save more money for lens :)

These cameras differ vastly, and it may be worth considering what style you want a little more, rather than which camera is right from this selection. Small cameras are more fun to use, they don't dominate you and easier to carry around. A DSLR style camera will give you lots more control, quicker control, and added features, but the cost is size and weight. 

Given you are not sure what type of camera you want, I would recommend the NEX-7 (or similar size) as it is far more portable than a DSLR sized camera, same sized (I mean dimensions, mega pixels don't really matter too much) sensor, especially for parties and travelling. I would also look at the NEX-5N.

If you want to take photo's of parties, and I'm assuming we're not talking about a kids party, you will get lots of attention with a big camera. It does that and you might like it. The downside is you're left dragging the thing around the whole time. Everyone wants to have a go and accidents/mistakes/theft happens, drinks spilled, can't relax. A smaller camera is more fun, it doesn't dominate. For that I use a Fuji X100, about the same size as a NEX, with a 20mm f/2.0 lens. Beats carrying a big DLSR around for those times. A NEX-7 with a fast (e.g. f/2.8, f/2 or f/1.8) wide fixed (prime) lens (somewhere between 20 to 35mm) will sort you out for parties, nights out, family stuff, friends and more. These lenses are usually quite flat, so the whole unit can slip into a pocket or small bag. For travelling and other times, that super zoom or similar is handy.

Consider DSLRs from Canon and Nikon, or a small form Olympus PEN camera - which has a great market for second hand lenses as it's one of the most popular.

smaller size, portability, probably the same sensor inside