I found the easiest way to find shorts that drain the battery was to connect a brake light or head lamp bulb...
This is an excellent method. If the bulb doesn't light up you don't have a short but you may still have a higher than normal current drain. In this case, add a multimeter on the amps range in series with the bulb as well, so that the bulb protects the multimeter in case anything tries to draw an excessive current.
Leave the car for a good few minutes after connecting this, as the Omega has electrical items that take a few minutes to shut down. The current reading should settle down to a few tens of milliamps. Certainly current draw of over 100 ma is cause for concern as it will cause the battery to flatten when left idle.
If you find excessive current draw, it's a case of removing fuses until you find the circuit at fault.
Regarding checking the charging, you need the multimeter on the volts range (double check it's NOT on amps) and connect it across the battery terminals. You should see 12.5 volts or more with the car off and no electrical items on with a healthy battery. Start the car and the voltage should build up to 14 volts or more at a fast idle. More than 14.5 volts indicates an overcharging situation due to a faulty regulator in the alternator.
Once the voltage has stabilised, turn on a few electrical loads (e.g. headlights, heated rear window) and check the voltage doesn't fall significantly (say below 13.5 volts).
If the charging voltages look low, your problem is probably that the battery is not charging sufficiently when the car is being used. Suspect the alternator or the wiring between it and the battery.
Kevin