If the stairs were previously varnished under the carpet, maybe you can just clean the smell off with a strong detergent. If unfinished, I think a sealer is needed to cover the absorbed smells. Shellac is really great a sealing odors, and is more easily removed than varnish or poly, or stain for that matter. You may want to paint the verticals (risers) and stain the treads, that's a classic look, then add the runner.
Casey

Sounds good, What sheen of white paint should I use?

Sheen; match whatever the other trim in the vicinity is wearing. Semi-gloss is the standard.
Casey

Just a thought what about DURA seal water based stain Can that be used?? If hardwood floor stair treads were to be installed at a later date. I doubt it would make a difference what I use. I'm putting this I assume on Pine, or whatever they made prefab stairs in 23 years ago? Thanks