Hey again Earthmama2010,
I hope your bathroom floor and mouldings turned out okay, let's get that wallboard strip off.
I'm with you with taking out the strips, it seems like they are just magnified if you simply paint over them. First off, I'd recommend to use a sharp utility knife to cut any caulk, paint, or sealant lines where the strips meet the wallboard, if there are any.
If there were was any sealant or adhesive holding up the strips, this will now make it easier to pry them off without doing any significant damage to the wallboard itself. If you can get some access towards the bottom of the strip near the floor, you can use a flat pry bar to take off the strips. Be careful at this step, you'll want to take your time and do as little damage to the panels as possible. Below is a link and image to one that I recommend for you to use.
After getting the strip off completely, now you can see how big of a gap you have between the panels. If ithe gap is under an inch, I'd recommend to use a very strong spackling compound to effectively fill and cover the gap. The one shown below is so strong, you can use it over metal!
It can applied just like any putty or spackling compound using a flexible putty knife. Any gouges or tears on the wall need to be removed or addressed before applying this. You may have to do successive coats to ensure the gap is filled. Make sure each layer is dried before applying another coat, and you can then sand down the area with a sanding sponge afterwards.
A good oil-based primer can be used on top of this as well as your wallboard to ensure whatever topcoat paint you have (even if it is water-based) will look and perform great for years to come.
Hope this helps you out,
I would treat the gaps which remain after removing the strips almost as if they were drywall joints. Rather than using drywall paper tape, I would use the yellow, self-adhesive fiberglas mesh tape. The yellow tape is thinner and requires less build-up to hide the thickness of the tape. This is important since there are no recessed edges for taping as with drywall. You do not want to see high ridges over the seams.
The self-adhesive feature of the fiberglass tape means that no build up of drywall mud is necceassry to embed the tape. This helps keep the patched area thinner. The open mesh allows the mud to be forced right through the tape into the seam.
For patching, I would initially use an easy sand "hot mud". The hot muds do not schrink and will dry rapidly, regardless of how deep the patch, as they dry chemically. Hot muds tend to have superior adhesion, feathering out nicely. After the hot mud is dry, feather out the joint using drywall topping compound and a wide blade drywallers' knife. This is to lessen any perceptible high ridge.
After sanding with a sanding block using about a 120 grit paper or screen, spot prime all the seams with a good acrylic primer such a Behr's Number 75 or Glidden's Gripper. Next, prime the entire wall with the same primer. The primer can be tinted toward the finish color. Finally, paint with the color and sheen of your choice.
Water soluble primers can be used with these wallcoverings because they are not really wallpaper, but patterned plastic coatings glued to the substrate with non-water soluble adhesives at the factory. The matching patterned strips which hid the gaps in the wall are what attest to the fact that it is not really wallpaper. These products are used commonly in the mobile home and RV industry.
In a former motorhome which I owned, I actually removed the strips, patched the seams and hung a less garrish patterned vinyl wall covering right over the factory faux wallpaper, after sealing the wall with a bonding agent.