It is possible to paint anything. The question becomes how much time, effort and chemicals are you looking to invest in your space. The first thing is: determine what type of finish is on the staircase and doors (oil/solvent vs. water based stains). Normally wood is finished with oil based products...but not always. The next thing is: do you want to paint (ie remove the look of the wood) or do you want to refinish with a darker stain? Painting is faster but will remove the look of wood grain from the banister and door (please don't paint the stair treads if you can avoid it...it takes a real flooring professional to get paint to stick to wood flooring). Refinishing requires stripping the old finish and staining the banister and door the same stain. Then comes the problem of what are the wood species underneath and how will the wood (if different from each other) retain the stain you have chosen.

These are all questions that would need to be answered before approaching a wood "refinish". So long as you have the right chemicals (paint primer) you can make any paint grab any surface - so long as you have access to a paint expert or even better a professional painter who specializes in what you want done.

Thanks so much for your replay. It's definetely finished with oil, how do you remove it before you paint it? And i do want to keep the look of the wood, i don't want to look like i painted it. So i guess i need dark stain. Can you recommend brands for stain and for primer?