It is a bit late now, but you probably should have used a light coat of shelac / oil *before* the stain. It would have prevented the stain from soaking in deeper in the more pourous areas and given the cabinet a more even finish. I think most plywood would be made from pine or other softwood, and that wood tends to soak up the stain in an uneven fashion.
If you want a natural wood finish, you could always get a nice quality hard wood veneer and glue it on and then stain the veneer to the desired color.