I mostly just use white vinegar. For general cleaning, I just have a spray bottle with a vinegar and water mix, I spray the cage down and wipe it up with paper towel.
If the cage (or litter box) is more dirty, I wash it with regular dish soap, then use the vinegar. For really bad urine stains, I soak it in strait vinegar and scrub a lot. Make sure to rinse well to get any residue off, but vinegar should not pose a problem.