I would say no ceramic tile if you are working with unstable joists and or sub-floor. OSB/particle board is a terrible substrate (not to ne confused with sub-floor) for tile. As you have seen, it's unstable and swells when wet. Plywood is not much better.
Industry standards require a solid joist arrangement > and a minimum two layers of plywood 3/4 plus 3/8 for a total 1 1/8. On top of that a suitable substrate such as cement backer-board underlayment (CBU) - 1/4 inch will do. The backer board should be mechanically fastened with backer screws and embedded in a layer of thinset. A suitable substrate such as CBU will have properties that keep it from swelling with the seasons and working the tile loose. The multiple layers of plywood/CBU will provide a "cleavage" layer or break from house/joist movements.
All that said. You MIGHT get away with less than ideal conditions in a small area in front of a door. The joists are less likely to flex near the foundation. But you better clean up, patch and re-fasten the OSB and get a good layer of b/c (don't use CDX sheathing -it has voids) plywood over the OSB. I wold go 1/2 minimum or 3/4 if you have the room/height.
Use a good quality latex/polymer fortified thinset that will give you a little more protection against movement. Don't use the cheapo 8 dollar a bag stuff.
You can prime the plywood before attaching and embedding the backer-board to protect against water infiltration damage.