The AVI files the G2 makes are only 320x240 pixels, DVD's are 720x480. Video tapes are in the 400 range. When you start out with a low resolution source like the AVI's from a camera, there is nothing you can do to make it look clearer, even by encoding it at a higher resolution. It just doesn't have the data there to create a clear picture. You can, however, cause the source to degrade even further by lots of MPEG encoding. You should take the AVI and only convert it to an MPG once, after editing. If you convert the AVI to MPEG then edit it, then each time you make an edit your happy with, you probably save it, which re-encodes it. MPEG is like JPEG, its a 'lossy' compression method. Each time you save the file it looses a little more data, and makes it a little more blury than before. AVI doesn't compress the data using a lossy method, therefore you can save an AVI over and over, and not loose any picture information.
You probably got much better results by capturing video tapes to your PC, due to the higher resolution of the video tapes to start with. Remember, this is not a camcorder. It can take short, low resolution movies, but they are really useless for any serious purpose. Its nice to have in a pinch, but I never use this camera for video. The video feature was probably just an engineer realizing they could capture a low-res video file by dropping the pixel count so low that you can get a reasonable clip (30 seconds) before the camera has to flush its memory buffer to the CF card.