If it's wood, you won't ever get it completely clean. Bleach or vinegar about the best options for neutralizing/removing the calcium stains. Just make sure to rinse thoroughly with clean water, especially if you're using bleach, as you don't want that to stay in the wood.
Don't expect to be able to make any cage look like it's brand new.
An all-wire cage can be cleaned very well with a propane torch. But, if you don't have one, then try soaking any calcium deposits in CLR, and then scrub well with a wire-bristle brush.
Usually as long as the cage is mostly clean, using bleach or other disinfectant, rinsed thoroughly and given a little time, it'll be safe for the next bunny.