Back stairwell and landings essentially done
After several hours of stripping and sanding the stair treads and landings the results were still somewhat ugly so I decided a different solution was required. With a little online research I discovered a technique that provides a pseudo-stain like finish and decided to give it a go – worst case is I would just paint the steps and floors a boring color.
Here are the steps and landings pre-finish:
The step treads were a blue-gray color. The 2nd picture is after the vinyl was removed and the 3rd after the glue was sanded.
The re-finish technique required the base to be painted a color similar to oak:

Then you apply a gel stain and brush it to get a wood grain look:
I am very happy with the results for a back stairwell but would not do this for a front staircase.
Here are some more post pictures:
In the 1st picture everything has been painted – including the purple plumbing primer on the pipes. The 2nd picture shows how the gaps around the pipes in the ceiling have been closed (and it shows the door to the laundry room). 3rd picture shows the “bulk-head” for the outside stairs to the basement. 4th picture is of the water damaged corner. The drywall for the ceiling has been finished as the leak appears to have been fixed.
Here is a repeat picture of the water damaged corner:

So the tile ceiling and damaged plaster have been replaced with drywall and the vinyl flooring has been refinished. Still need to install some baseboard trim and corner round but that should not take too long. Then onto the exercise room.