The cracks come because the plywood expands and contracts with
the weather. It is possible to put something in the cracks that would
compress and expand with the changes. Good caulk should do this.

From your description, however, it sounds like the job is not
a good one so trying to make it look good will be a hassle.

You can put drywall over the plywood. You're right, it will
take some skill and ingenuity to make look good around doors and
windows.

If you don't think your skill level is up to the job, it's
probably not. Drywall take a while to learn to do right. If I had
this problem, I would hire a professional drywaller but tear out the
plywood myself, thereby keeping costs down.

One good reason to replace the plywood is that drywall has
fire-protection value that the plywood does not.

Peter