Hi Joyce, Welcome!
As Dave mentioned, you can't tile on top of hardwood, an it is also important to make sure your area is suitable for tile.
As for removing the linoleum, have you tried cutting it into strips with a utility knife (about 6" apart)? This is followed by peeling away the top layer (it will separate from the bottom). Once the backing is exposed you have two options. You can try soaking it with water and see if it softens enough to be scraped off. If this is unsuccessful, I have used paint & epoxy stripper (that contains Methylene Chloride), painted it on the backing, then razor scrapped the backing off the substrate. The chemical removal is dangerous and requires plenty of ventilation, protective clothing, gloves, and eye protection.
Personally, I'd just consider removing the hardwood, and start from scratch.