The answer depends on the depth, the distance from the bottom and the distance from the surface.
The explosion goes off, the water vaporizes and you have a bubble.
The bubble is under pressure from the surrounding water and starts to collapse.
The pressure inside the bubble builds up and overshoots the surrounding water pressure, so the bubble starts to expand. Some energy has been lost so the bubble doesn't expand as much as it did the first time.
Now the bubble over expands and the pressure is less than the surrounding water pressure so the bubble starts to collapse.
In the meantime while this oscillation has been going on the bubble is rising, because bubbles are buoyant.
O.K. so what happens at the surface? Well, it depends on the phase of the bubble: is it expanding?, or is it contracting? or something in-between. In some cases you could get a big jet of water, and a disruption of the water surface. If the bubble doesn't reach the surface then not much would happen, although the shock wave still propagates.
It also matters how far the explosion was from the bottom (or the surface) in terms of initial conditions. If you are several bubble diameters away from the bottom, it probably doesn't matter as much.
The bubble, it rising and oscillation is a slow process compared to the shock wave of the explosion. The shock wave will radiate from the explosion, Probably at the speed of sound, and can reflect off the bottom or surface, it is a pressure wave so you can have constructive and destructive interference effects which depends on the geometry. If you are far from the surface or bottom, then the wave will look like a spherical wave until the sphere hits the top or bottom, then it is more complicated.
The radiation and light from the explosion will be strongly absorbed, Ocean water has some transparency in the blue/green, so the light from the explosion if it reaches the surface will be strongly filtered, and be mainly blue/green photons. Sunlight is pretty bright, but at 400 ft or so it is almost completely dark due to the absorption. You could do a calculation but if you are a few miles deep, I am not sure you would get a much light out the surface. Miles of water would also reduce energetic particles and radiation significantly. Note: that it doesn't impact the lifetimes of the radioactive materials, and whatever gets kicked up on the bottom and becomes activated may get transported by ocean currents. If the explosion is on, or near the bottom, the type of seafloor would be important.
There are a variety of references on the subject of underwater explosions, one that goes into some detail and availible online is https://ro.uow.edu.au/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=2563&context=theses
