Sanding with more than 150 grit can close the pores and prevent stain from penetrating. Plus, a stain will just penetrate a little below the surface of the wood, more so in less dense wood and very little in denser wood. Oak has two different grains with with those two different stain absorbing properties, so there will always be darker and lighter areas. You can try resanding, or try leaving the stain on longer---the dense part of the oak will absorb less while the softer grain will absorb more color.

Can you post a photo? I’m going through a similar dilemma and I’d love to see your floors. Our living room is white oak and the dining room and hallway red oak. We love the pale color of the living room and are trying to keep them all light. Houzz has made a few recommendations but we have not yet pulled the trigger. I still feel like I need more counsel.

Laura,,Poplar is more of a paintable wood rather than stains. to get a true ebony stain color you could try a black aniline dye first, and then go over it w/ebony gel stain. I did it with my oak and got it very black. otherwise, just use a good enamel paint for wood in the same black color as the wall. and no, stained wood doesn't necessarily mean it will hold up better. if the handrail is properly prepped, paint should hold up fine. But try the ebony stain first, if you like. I also think Polyshades has a black stain/poly all in one.(I would still do the aniline dye first because it will give you a black base. poplar has a tendency to turn a little green. the black stain may not be enough to completely cover it. see table below)

Maybe, definitely yes, absolutely not, it all depends. How about pictures of the area in question? What other colors are involved, walls, etc.? Impossible to really offer much without context.