For how things would look to the superhuman, you have your choice. The human visual system plays a lot of tricks with color already to allow us to see what we do see wikipedia on color spaces So you could just say that this superhuman maps the wider spectrum to the ordinary color space, so they don't see any 'new' colors, but things won't look the same color to them that they do to us, and they'll have problems with things like photographs and video displays not looking right. Alternatively, you could say the superhuman gets a higher dimensional color space ( there are a few people who actually have this ),so they'd be seeing lots of colors people have no names for, and may or may not have issues with displays.
There's also the issue that you can't see details smaller than the wavelength of light you're using to see it, and you can't resolve images well if there isn't much light available. So infrared is going to look a bit blurry, and radio wave images will just be vague blobs. Gamma and x-ray will have the issue of there not being very much gamma or x-ray to light things up with, so anything you see with that will be super grainy and hard to make out - like photos taken at night but moreso. If you see a nice crisp image using gamma rays, you know you're getting a lethal dose of radiation!
Finally, you have the issue that we see things around us because light strikes those things, and more or less ricochets off them into our eyes. So light that's useful to see things with has to bounce off of things at large angles. Longer wavelengths move more like ripples in a pond; they tend to go around or through obstacles and continue on the direction they were going. Shorter wavelengths move more like particles, bouncing off of things easily. (That's why the sky is blue and sunsets are red - of the light passing overhead, it's the short blue stuff that can bounce down to you, and the long red stuff is what can pass through all that air between you and the horizon with out getting scattered away). Anyway, the super short wavelengths like gamma and x-rays move like bullets. A gamma ray striking a typical atom is going to drill right through instead of bouncing. So you could see bright sources of very short wave stuff like gamma and x-ray sources, and you can see through things if the x-ray source is behind something, but you can't really use them to light up an area flashlight-style. Same for very long waves - they don't scatter well either, so your superhuman could see that a radio tower was transmitting, but the transmissions wouldn't light up the area for him.