Sam, you didn't tell us the most important thing. What wood is used for the treads and risers now? I would not be at all surprised if you find oak under the carpet. Then it will just be a question of refinishing and patching the staple holes.
If you do have pine, you can buy preformed oak treads at your home center. These are 5/4 with a bullnose milled into one face. Depending on your stairs and your level of woodworking expertise, I would consider having a pro install them. I would not consider facing with oak plywood because you only have 1/16" of oak to start with. After sanding to finish, you will have less than that. Foot traffic will wear this out more. With the plywood, there is not enough oak left to refinish. Doing it with the plywood means that you would be doing it again in 10-15 years. Do it with solid oak and it will be good for more than 100.