In the 50’s plastic wall tile was used in a lot of homes. If you want to get rid of it, you might be considering removing the tile. That probably isn’t the best idea. The adhesive that was used in a lot of these installations is very tough, and you might even find that it is still not completely cured behind the tile.
A good option to address the old plastic wall tile is to cover it with decorative panels. Not necessarily panelling, but panels that are current and attractive.
In our case, we used beadboard panels from Georgia Pacific (the brand name is PlyBead. The panels are 3/8″ thick and installed easily by using a construction adhesive along with some finish nails to hold in place until the adhesive set. We didn’t do anything to prepare the plastic tile other than cleaning the surface. Since the panels were only 3/8″ thick, we did not have to replace the window or door trim near the panels. In many cases, you can find decorative wall panels that are from 1/8″ to 3/8″.
Another nice product option is called “Styleline” (again from GP). There are many decorative options for this product such as a leather look, or a linen look. I know that Lowe’s carries the product but I am not sure about Home Depot. The cost can add up if you hare a large area to cover, but the time to complete the project will be short.
Your only other feasible option is probably going to be to tear out the existing plaster or drywall behind the tile. The adhesive isn’t going to want to come off cleanly, so a complete demo is probably called for. If you choose this option take the opportunity to update wiring, plumbing and to insulate the walls that you demolish.