Ammonia is what normally makes the water look cloudy in a new tank. If you've got the same filter media that the Oscars had and it never dried out...then it should be cycled. If there was a lag in there and you didn't get these fish the day after getting rid of the Oscars, then we can assume it's not cycled. It takes about a month (give or take) to cycle a tank. The only thing I know of that can cause cloudy water is ammonia in an uncycled tank. Or perhaps something in your water supply. You don't have play sand in there, do you? Lots of times play sand never does clear up, mine never did and I had to take it out.
The API liquid test kits for ammonia, nitrite and nitrate can be bought seperately at PetsMart or Petco for about $7 a bottle or so. Or you can just get the entire Master Freshwater kit for $30 at PetsMart (less online). The only difference is the entire kit has a pH test in it also. Not worth the extra money. We need to find out if your filters are cycled/mature. I suspect they're not and that's your problem.
