The Hardwood Flooring Manufacturers Association says OSB is OK so long as it is 23/32 or greater thickness. The subfloor should be nailed, glued, and screwed.
K3, I believe, can swell, and as such is a no-no under tile. Same with MDF. If you take it down to the bare OSB subfloor, then you should add at least 1/2" of plywood. Mike Holmes would probably tell you to use Ditra as well.
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