So if I wanted to take a photo of a fast moving subject I would be stuck with 1/160th shutter speed.
I'm guessing your camera has a maximum flash sync speed of 1/160s.
You would only be "stuck" with 1/160s if you were using a flash/strobe to take the photo. If there was enough available light, you wouldn't need the flash and you'd just set the camera to whatever shutter speed you wanted.
Now, I assume you are using the flash because there isn't enough available light. There are three general situations where this would be the case. 1) The flash is pretty much the only source of light. 2) There is some available light but the flash is still the primary source. 3) You are using the flash to fill certain areas but still relying on the available light to expose most of the scene.
In 1), you can pretty much ignore the 1/160s of the camera as this will have almost no effect on the image. The effective shutter speed will be between 1/800s and 1/20,000s depending on the flash and the power setting. Note that when using iTTL/eTTL, the strobes are basically quenched when enough light has been received so it has the same end result as manually setting the right power level. Even 1/800s is going to be fast enough to freeze most action, especially under water.
For 2), you will get similar result to 1) unless there is quite a lot of available light. If you are shooting a subject relatively close to the camera, you can use a smaller aperture which will decrease the effect of the available light and so you may still be able to achieve relatively fast effective shutter speeds.
3) is the difficult situation with fast moving subjects. The 1/160s of the camera shutter is going to let enough light alone to expose an image and you're likely to get some motion blur. What you can do, however, is set the camera/strobe to rear curtain sync. Remember I was talking about the leading and trailing edges of the shutter? With rear curtain sync, the flash is synchronised with the trailing edge of the shutter (rear curtain) and so the flash effectively goes off at the end of the time the shutter is open. This will give you an image that is sharp and frozen from the flash, but with motion blur leading to the frozen image. i.e. it gives a sense of motion in the still image. You won't have frozen the motion, but you can have a pleasing image.
How do you work out what the "on" time of a strobe is at different power levels?
It is usually listed in the specifications of the strobe.