You are no where ready to stain. It all needs more stripping and then sanding. Get the strongest stripper you can stand. Sorry, but the stronger it smells the better it works. A paste stripper will cling to the vertical parts better. From the pictures I would say that you need to put the stripper on, let it work, scrape with a putty knife, wipe down with lacquer thinner. Do it all again if there is still old finish left. Once you think you have it all off, one more coat. This time brush it with a stiff synthetic brush, wipe down with lacquer thinner. Read the can directions, neutralize if needed.

Then sand, sand, sand. Start with 80, then 100, and maybe 120. Once it is all uniform, you are ready to stain.

It's going to be a lot of work, but a good job won't result unless you do the prep correctly.

As Al suggested... you've got a LOT of work ahead of you.

The "strippers" function is basically to remove the TOP coats/ finish that was in place... they'll do very little regarding taking all of the COLOR off the wood, which has penetrated the pores/grain of the oak.
Depending on how finicky you are as well as how good you want the results and how dark you want to go... is what will determine how much more elbow grease you need to invest.
You'll need to sand out any residue of the old stain as well as any finish you miss with the strippers, especially if you're leaning toward a light color. Any old finish that is missed, will NOT allow the new color to penetrate... and you'll have those pesky blotches.
The corners, & nooks & crannies such as under the nosing are the real PITA areas.
A steel "scraper" with a sharp edge is sometimes the best bet... but if you're not too handy, you can do more damage than good.

As a DIY'er, I'm sure you've made a few exploratory trips to the Big Orange Box..., next time you're there, go to the lumber department, and look at the unfinished RED Oak stair treads they usually have in stock... when you get the wood to look like that... (uniform in color) you will only be a few fine sandings away from ready to stain & finish.

You're working against the old finish, the old stain, and the work performed by the last guy who did the work... if he/she did a mediocre sand/finish job... you've got to erase that work as well.
Best of luck.
Be sure to post pics of your completed project!

Finally found someone to finish the stairs and two windows! Only changed me $1200 and they look fantastic!