Hi there,
The Canon SX230 is a great little camera like all of the Canon ones but a little underwater bird has told me that you may not be able to use all of the camera's functions if you choose a Canon housing, so it would be best to check this out with a supplier before purchasing. The camera's own flash will work brilliantly as long as you are nice and close to your subject, within about a foot (being careful of the coral and reef around you though). If you are looking to light a subject from a little further away, then you may prefer to use a strobe or if you would like to light up a larger area, i.e. the camera's built-in flash will light up a moray eel for example, and the strobe will help to illuminate the area around it too.
Without a strobe, you can still achieve lovely colourful shots using the camera's white balance feature, and using the Vivid mode, will really help to bring out those lovely blues and colourful corals too. You will need to have as much available light as possible for this to be effective though, so staying at about 20 ms and above in blue water conditions is paramount.
With regards to the video function, on most Canon's you are able to switch from stills to video whilst underwater, but again this is dependent on the housing, so again, do check with your supplier before purchasing. I would not recommend zooming whilst filming so there is a tendency for the wobbles to get into your lovely footage. Best to finish the clip, move a little closer to the subject if you can and then re-start recording, if you can of course.
Hope that this helps, I've written a book which is full of photos taken with all kinds of compact cameras and answers all of your questions in an easy-to-understand way and Backscatter may have a few copies left of it.
Otherwise, if you need any more help, just post away, happy to help on here too.
Wishing you the best of luck and look forward to hearing how you get on.
All the best,
maria