I was wanting to take some shots similar to the fifth one in the link. I was wondeing roughly what settings would be needed to achieve this? I am trying to wrap my head around it, would you need a fast shutter to "freeze the streaks, or a slow shutter to allow them to be more prominent? Is this something bought out post production? and lastly what role would aperture play in the shot besides depth of field?
Recommend you check out the original website where the original image was posted - UnderwaterPhotography.com. Lots of great folks there.
I was taught to use higher shutter speeds to stop the rays. 1/400th or higher is typical shooting with no strobes like the image you asked about. With strobes you can try shooting at the highest shutter speed that you can sync (1/250 or so) and use a low ISO and f/16 or 22 to limit the exposure so you don't blow out the bright rays.
Sunbursts are a blast to play with and there are lots of variables so no one way will work every time.. I'd recommend keeping the shutter speed high, work shallow if you can and shoot early or late in the day to have the best opportunity.
Good luck,
Steve
While not the best example, I got this one using the settings Steve suggested: 1/250, F16, ISO100 using D7000 & Tokina 10-17 Fisheye with two Z-240 strobes.