I agree with Oldog/Newtrick. What you have in those pictures is NOT hardwood flooring that just needs to be refinished. It's 1X6 fir boards that form the sub-floor in your house.
Typically, in a house you'll have the floor joists. Then the subfloor will be installed and will consist of either 3/4 inch plywood or 1X6 lumber nailed either perpendicular or at a 45 degree angle to the floor joists. Then all the interior and exterior walls are built on top of the subfloor. Then, "underlayment" which will by plywood or particle board between 1/4 and 3/8 inch in thickness will be nailed down over the subfloor in each "room". Then, after everything else has been done, the finish flooring (carpet, sheet vinyl, laminate or whatever) is installed on top of the underlayment.
The purpose in having that underlayment is to prevent the joints between the sheets of 3/4 inch tongue and groove plywood or 1X6 lumber boards from "telegraphing" and showing through onto the new finish flooring. However, an important advantage in having that underlayment layer in there is so that if push comes to shove, you can always remove the old flooring by prying up and disposing of the old underlayment, and installing new underlayment for a fresh start. That avoids all of the difficulty in removing old flooring that's securely glued down to the underlayment.
So, if I wuz you, the first step would be to nail 1/4, 5/16 or 3/8 inch fir UNDERLAYMENT over top of your fir 1X6 subfloor. (Fir underlayment will look identical to fir plywood. The difference is that fir plywood is allowed to have voids in it's interior plys, whereas in fir underlayment, any such voids are filled with water putty to prevent "soft spots" on the floor that could cause trouble under the finish flooring. In my view, the BEST underlayment you can get is fir underlayment (which looks just like thin fir plywood) or "Baltic Birch" which is a furniture grade hardwood plywood that comes in metric sizes from Russia.
Go to Johnsonite > Home
and click on their "Stairwell Management" link to get to this web page:
Johnsonite > Finishes & Accessories > Stairwell Management
Once there, click on the "Download the Stairwell Management Brochure" link on the right side of the screen.
Go to the last page of that 8 page brochure to see the vinyl stair nosing profiles available in 48 different colours from Johnsonite. Note that the VCD-XX and SVCD-XX-A have lips that will accomodate either 1/4 inch thick or 3/8 inch thick flooring, respectively.
So, one gameplan would be to order the vinyl stair nose moldings from any carpet retailer or flooring supply store and install them on your stair nosings.
Then, make templates of the stair treads and risers from cardboard, and use those templates to cut out pieces of laminate or carpet to match the size and shape of the template. Then, just use masking tape to mask off the tread or riser so that you don't have to be as careful spreading the glue with a trowel. Then, tuck one end of the finish flooring material into the lip of the nosing and press the flooring material into the tacky glue.
And, of course, having nailed underlayment over the stair treads and risers, removing the old glued down laminate or carpet on the steps will be easy since you can always pry the old underlayment off with the finish flooring still stuck to it.