What is the best way to lay vinyl over old hardwood floor covered in flooring adhesive?

I ripped up the vinyl floor in my bathroom because when whoever laid the floor last did it, they didn't bother to secure the floor beneath it. It appears that several floorboards are cut off before the joist so they bob a little. My question is, after I secure these, what is the best way to lay new floor? My dad said I should just lay quarter inch plywood on top of the adhesive left over from the last floor and just screw it down then lay my new vinyl over that. But with that I worry about pockets that could crack in the future. My father in law said I should spread floor leveler or get adhesive remover but with both of those I'm a little worried it would seep through since I don't think the hardwood floor is sealed very well if at all. Any suggestions on the best method for this situation?