From the model number of the camera, it looks like it's a still camera which can also record video. Is it like the one in this ebay link ?
Sony DSC-H3 ebay listing
If so, the video quality is not going to be particularly good to start with. According to the spec (assuming that is indeed the camera you're using) it records video in MPEG1 (640 x 480 @ 30fps • 640 x 480 @ 16.6fps • 320 x 240 @ 8.3fps).
I've noticed a similar loss in quality when using Windows Movie Maker to export this to AVI or WMV.
The camera looks like it's excellent for still photos, but if the video quality is not acceptable, even at the highest export settings, all I can suggest is looking for a cheap mini dv camcorder which should produce far sharper videos (which if you're careful, you might find for less than the cost of the camera you currently have).