1) Chances are that it's two layers of 3/4 inch plywood. In any case the hardwood floors are probably 3/4 thick on 3/4 subfloor. Remove the linoleum and the top layer of plywood. Use a reciprocating saw to cut the plywood around the edges of the walls. Then put down a layer of 1/2 inch durock and tile on it. This will bring you to the level of the hardwood floors. The 1/2 inch durock + morter + 1/8 inch thick tile = 3/4 inch
2) Remove the linoleum and any adhesive that is remaining with a adhesive remover. Prime the plywood with a good exterior oil based primer. (This will keep the wood from sucking the water out of the morter to quickly.) Then tile. If you do it this way your finished tile will end up about 1/4 inch above the hardwood floor