Certainly, application of any paint will reduce, if not eliminate the odor coming from the plywood. But to be certain, apply an alcohol-based (pigmented shellac) stain-blocking primer. This type primer is used for blocking odors from smoke (fire-damage). You will have to ensure plenty of cross ventilation while applying the primer, because of the alcohol in it. Keep window open, set up a fan, and preferably wear a respirator that is designed to block solvent fumes. Extinguish all fire sources. Equipment cleans up with denatured alcohol (not paint thinner or water). Once the primer has dried thoroughly, the odor will disappear.
Apply the primer with a 2 1/2 inch polyester brush, or with a 7" roller with a 1/4 inch synthetic nap. Then apply either a conventional quality interior latex paint in an eggshell or satin finish, or use one of the new very low odor interior latex paints. If you don't want to deal with the alcohol-based primer, then second choice (not quite so effective against the odor, but probably would be adequate) would be a latex universal stain-blocking primer. Two coats of primer would be better than one. Keep in mind that much of the odor may be coming from the back side of the plywood, so consider priming and painting that, as well.