You definitely need to do some major water changes, and get some ammonia reducing products; your tank IS cycling at the moment.
Ammonia, as everyone said, is MAJORLY deadly to fish. Burns and destroys their gills (as was said before). Personally I recommend a big water change; like 50% asap. Then daily changes of small amounts (maybe 10%?) till your ammonia is converted to nitrite then nitrate. Nitrite is also deadly; it takes the place of oxygen in the bloodstream and suffocates the fish, so don't stop when your ammonia levels go down. Wait until the Nitrites also lower. Nitrates, in VERY high amounts, can be deadly as well, but amount up to 40 ppm hardy fish can handle. The problem with frequent water changes, is it takes a LOT longer for the cycle to complete; keep in mind the bacteria needs the ammonia and nitrites to reproduce: more bacteria = more reduction of ammonia and nitrite. However, whats more important? Getting the tank to cycle quickly or live fish? I prefer live fish myself *grin*
You will probably want to use an ammonia reducing product. Problem with those is you won't be able to test for ammonia then. The products binds the ammonia so it is no longer toxic, but do not get rid of it, so most ammonia tests still come up positive. Thing is, you don't know if you put in enough to combine ALL the ammonia, or you are getting a mix of bound and the deadly type. Its a tough call, but one I would probably chose to do as well; combining that with the water changes should keep your guys alive.
You may also want to look into what they call "bacteria in a bottle". Cycle and Bio-Spira are 2 examples. They are basically the bacteria your tank needs to get the nitrogen cycle going. I've heard positive and negative about Cycle..works for some, not others. May be due to the how long the bacteria can live in the container. I've heard great stuff about Bio-Spira, but its hard to find.
You can read more about the cycle here:
http://www.skepticalaquarist.com/docs/nutrient/nitcyc.shtml . The article can be a bit technical, but I think you can handle it.