remove them along with the vinyl and the luan that is probably under that. Only in certain scenarios would I consider going over vinyl with cement board and since I cant visually inspect your floor there is no way I would give a blanket ok on that one. Vinyl and luan offer no structural strength to a subfloor and many homes are built to minimum standards so what you have for a subfloor may not be up to standards to support a ceramic tile installation. We would need to know, assuming this is a wood floor because you only put cement boards over wood subfloors, what the size and spacing of the floor joists are, the length of the unsupported span of the joists and thickness of the subfloor and what kind of plywood it is. Particle board has no place in a tiled situation, CDX ply cannot be used as it is not rated for underlayment, the American Plywood Association (APA) gives it a sheathing rating only, means its good for the side of the house but not on the floors, OSB is ok as long as it is covered with cement board, plywood with a BCX rating is best.