The shape distortion you're seeing (especially in the right picture) is probably related to how you're drawing the texture. Ensure that you're using dimensions that maintain the aspect ratio of the image.
The blurriness is probably from the import settings of the image. By default the image is put through a bi-linear filter, the maximum resolution is 1024, the image is stored as a power of 2, and compression is enabled. All of these settings can cause what you're seeing with image quality.
In your case I'd say go to the texture importer and change the import settings for "Texture Type" to GUI (Editor/Legacy)
, change the "Filter Mode" to Point
, the "Max Size" to what ever is closest to your native resolution, and change "Format" to Truecolor
. Experiment with the last step of changing the format, since Truecolor is no compression whatsoever, and the image will take a large amount of memory.
Also look at tutorials for ways you can "coerce" the image into working well with compression by codifying the colors you use a little.