My daughter recently bought a 90 year old twin in the Roxborough neighborhood of Philadelphia and every flat surface was wallpapered! The Wagner Xtra Power Steamer has been the best tool for removing all types of wallpaper and multiple layers of wallpaper.
I first looked in to renting a commercial steamer for the job but this handy tool is only $55 from Home Depot, lightweight and very maneuverable. I bought the Xtra model because it comes with the smaller steamer plate shown in black in the photo--it is very easy to use between windows and other small, hard to reach areas.
The tank holds about a gallon of water and heats up in 20 minutes or so--faster if you fill it with hot water. The steam lasts 60-90 minutes. The hose between the tank and steamer plate is long enough that you can sit the tank in one place and work around most rooms without repositioning the tank. In the online reviews users complained that the unit does not have an on/off switch--I plugged it into a power strip and solved that problem.
We were not worried about mess on the floors because they are being replaced but if you have good floors you will need to cover with plastic because it does drip and sputter. You will also want to have a bucket handy to hold the steam plate when you put it down.
We were able to remove the wallpaper in all three bedrooms, the LR, DR and bathroom in a matter of days to reveal beautiful plaster walls beneath. I'm sure it will make short work of pesky outdated borders!