Remove dirt and grime from a knotty pine wall with a degreaser, such as trisodium phosphate, commonly known as TSP. Wear rubber gloves and safety glasses when handling TSP. Dissolve a half-cup of TSP in 2 gallons of warm water in a 3-gallon bucket. Clean the wall with a sponge dampened with the TSP solution. Let the wall dry.
Lightly sand the wall with 220-grit sandpaper if the surface is glossy. Don't overdo the sanding; just roughen the surface so that the primer will stick to it. Wipe the wall with a dry rag to remove any dust left behind from sanding.
Pour the oil-based primer into a paint pan; make sure you have purchased one that prevents resins from bleeding through painted wood surfaces. Apply the primer to the wood knots with a nylon bristle paintbrush. Use a paint roller with a natural fiber cover to coat the entire wall if knots cover most of the surface.
Allow several hours for the primer to dry completely. Test for dryness by ensuring that the surface doesn't feel sticky.
Sand the areas you primed if they don't feel smooth after they dry. Remove dust from the sanded surfaces with a dry rag. Paint over the primer within a week to avoid a buildup of dust and dirt that interferes with the paint's adhesion.
Apply one coat of satin or semigloss latex paint to the wall with a roller that has a nylon cover. Add a second coat after the first one dries if the first coat doesn't completely cover the primer.