Is your TV 720p or 1080p? It sounds as if it's only 720p/1080i (based on the "native resolution" detected by your computer on VGA), meaning that the highest possible resolution you could achieve WOULD be 1366x768 @ 60hz without switching to an interlaced refresh rate, such as 29/30hz, which in turn would degrade the picture quality considerably, and add the flickering/vibrating you mentioned. So it sounds like, with your particular setup, using the VGA cable is the best option, and there wouldn't be any real benefit to using HDMI.
Also, check your wide mode/picture size settings on your TV. Most will default to a "Normal" setting that's designed for broadcast HD content, which is what causes part of the screen to get cut off. If you switch it to a different mode, such as "Full" of "Full pixel", it will display all of the signal, without cutting anything off, and without the need to use overscan settings in your Nvidia control panel.