Hi Rachel,
I have a design build firm here in Jacksonville Florida. I generally would advise you to lightly sand everything first ( rails, post and the banister trim) to break the varnish. Then use a liquid sander deglosser to help break the varnish down even more. Wipe everything clean with a tack cloth. Apply a primer coat of gripper primer usually made by kilz. Then after that drys apply your top coat of oil base. If your on a tight budget. Sanding the treads is most likely the best coarse of action to take. Any floor refinishers know the process and can make it appear the same. The issue is that the material varies from oak to maple. I hope that helps and your project goes s
Q