I honestly have no idea what you are talking about, but maybe you are simply ignoring sub-pixel positioning, which would resample your images? Naturally, with images that small this would become pretty apparent. Check your numerical values and make sure they fall onto whole pixel values. Otherwise provide screenshots.
200 x 200 is awfully small for a HD comp. You will need 10 of them to make a single row in an HD comp.
To make life easier all of your images should be an even number of pixels wide and high. The images should be sized so that they will be at 100% scale when they are in their hero position. Hero position is when you have the most important part of the image exactly placed where you want it in your composition.
You should also be using only the square pixel presets for composition settings. You must have a good understanding of the technical aspects of video formats and compression if you want to create any custom composition. If you are creating a custom comp that should also be an even number of pixels high and wide.