I glanced at the pdf linked by J above but didn't read it too closely so don't listen too closely...
As a "quick" (depends alot on how many relays there are) check, consider having someone turn things on and off while you feel one or two relays to see if they engage/disengage. A relay typically makes a click noise that you should be able to feel with your fingers. Use both hands, each on a different relay. Initially, use small yellow office "stickies" to label the relays while the other person takes notes or uses similar labels. From this, build a map or table of which switches/relays control what.
This gets easier after each test, since the number of switches/relays/circuits is reduced after every test.
Make a sketch of the physical location of each relay and label it based on the stickies. Number the relays on the sketch and physically.
Once you've isolated the relays that do work, you can add the ones that don't to the table as unknowns. Then replace a nonworking relay and test the nonworking switches to see what circuit starts to work. Add the now working switch/relay/circuit to the map/table. Repeat until everything works and never lose the table.
If you can't feel the relays engage, you need to test them by for example measuring the voltage across the coil.
This is of course tedious but once done, its done forever until the wiring fails. X switch doesn't turn on Y lights? Table says Z relay.
Why the relays fail and leave the device/light on is a question. Were the relays wired to use normally closed or NC contacts, even though it makes little sense?
I've subscribed, so if you want to chew me out for such a simplistic approach, feel free