Linoleum and plywood can be a nasty couple. They can separate and grow apart. They always seem to work at cross-purposes. The problem arises when installers overlay the existing floor with 1/4-inch plywood. The subsequent linoleum placement seems fine at first, but then everything gets spongy and feels anything but solid. Getting the linoleum off is not a big deal. The problem arises when the plywood has to go. It's usually stubborn due to thousands of staples that cling tight to the floor. Separate them now, or forever hold your peace.
Insert a screwdriver behind any baseboard around the perimeter of the linoleum. Pry it loose and remove it.
Insert a putty knife under any loose flap, corner or seam of the linoleum. Lift it as high as possible. If it continues to lift easily, continue pulling it off. When it begins to resist, squirt acetone under it. Allow the acetone to dissolve the glue for one minute and continue lifting.
Cut strands of glue loose using the putty knife if needed. Continue lifting, adding acetone and pulling off the linoleum. If it comes off in sections, repeat inserting the knife under a new flap or seam and repeat the procedure until all of the linoleum is removed.
Hammer the tip of a flat pry bar under any loose seam or edge of the plywood underlay. Pry the plywood up enough to grasp it with your hands.
Pull up on the plywood section evenly. It's stapled securely to the floor on both sides and around the perimeter. Rock the plywood back and forth to loosen the staples. Continue pulling up as evenly as possible. Attempt to get the staples to come out together.
Insert the pry bar under stubborn spots and pry up. Continue lifting. If the plywood resists and breaks off, that's fine. Repeat Steps 4 and 5 with each broken part or section until all of the plywood has been removed.
Remove any staples that did not come off with the plywood using locking pliers. Clamp the end of the staples in the pliers and rock them back and forth to lift the staples. If the staples break off, use diagonal pliers to remove the broken pieces. Some of the broken staples may not be removable. Hammer them down instead.
Scrape off any dried glue using a glue scraper. Sand the floor to remove any residual debris, glue or broken staples using a belt sander with an 80-grit belt.