We are considering a visit to your bathroom instead of our upcoming trip to London. If your letter is any indication, we can expect much the same kind of environment. On the other hand, if Palm Springs is more your style, then, fear not, help is on its way!
The peeling paint and weeping walls are a clear indication of the need for improved bathroom ventilation with the installation of an exhaust fan. If you're handy around the house, then this may be something you wish to attempt yourself, along with a well-illustrated do-it-yourself manual and a permit from your local building officials. If this seems like a challenge than you are willing to take on, try calling a local electrical or heating contractor. Not only will the space be more comfortable, chances are your paint will stop peeling.
As far as your ceiling is concerned, it sounds like it is beyond repair. Your best bet is to apply a sheet of 3/8" drywall over the existing ceiling. You'll want to attach it with drywall screws that are long enough to penetrate both layers of drywall and attach securely to the framing. Next, pick up a container of drywall joint compound and some joint tape. (Turn to the section on finishing drywall in that do-it-yourself manual we mentioned earlier.) Again, if this is not your forte, now's the time to enlist the services of a professional drywall contractor.
Finally, give the soiled walls a good washing with TSP (Trisodiumphosphate). Apply a coat of oil-base primer to both the walls and ceiling, and follow it up with a finish coat of an oil-based semi-gloss enamel.