You are asking two different things: you want an aspect ratio of 16:9, but you also want a resolution of 1024x768. The problem is that 1024x768 is 4:3, not 16:9. If you want square pixels (proper aspect ratio), then you have two choices: either run 1366x768 which is a 16:9 ratio, or run 1024x768 with black bars on the sides.
If make the 1024x768 fit into only a portion of the screen horizontally, this way it will appear at a 4:3 ratio but you will be wasting a lot of your screen area. In addition, if you use this mode a lot, the phosphors in the center area of the screen (covered by the 1024x768) will wear more than the ones at the sides, where the image is black. This burn-in is very common amoung widescreen CRT owners, and your plasma screen is certainly not immune to it. Yes, plasma screens do in fact use phosphors as the fundamental method of generating light. They use a plasma discharge in a small cell (per pixel) to excite the phosphor, instead of a beam of electrons as in a CRT.
To do this, set up a custom resolution at 1366x768 in powerstrip (some video cards and/or drivers have this res already available). Now, click 'lock total geometry', and adjust the horizontal size to 1024. You will notice that the front and back porch values will be unusually high; this is normal, since the 'porch' is the blank area before/after the picture, which is large in your case.
Instead of using powerstrip, you could run 1024x768, and go find the geometry adjustments somewhere in the advanced section of your display properties (different for each manafacturer or driver provider). Use these to adjust the horizontal size of the image down until it looks like you want it. The video card drivers accomplishes these adjustments by adjusting the 'porch' values on output. Depending on the video card or drivers, you may not get enough adjustment out of this control to achieve a 4:3 ratio.