Are your test kits expired? What brand are they? Are you sure they are for saltwater? That is some gnarly water quality for a stocked tank. A water change is the safest and easiest way to bring down ammonia content, and some products like Amquel and the like can do it chemically. Probably both would be best...
First things first, make sure your reading are correct. You should check the expiration date and retest if they are still good. If you have some extra cash, having two different brands of tests provides a basis for comparison. If things are still nasty, i.e. ANY Ammonia (NH3) or Nitrite (NO2), plan on doing a big -maybe %50- water change.
As far as the corals go, what kind of light do you have, and how much work do you want to do? You can keep ahermatypic corals, those that lack zoanthellae, the symbiotic bacteria that produce nutrition for the coral through photosynthesis. Because they lack the ability to garner nutrition from light, they must be fed, which is labor intensive and destroys your water quality. There are also a lot of corals that tolerate very low light. There are plenty of Zoas and mushrooms that can hang.