After 200 meters the ocean is practically opaque. Objects much deeper than that are reflecting a handful of photons. Below 500-1000 meters you're talking about photons per second at the surface.
Water is one of a quite small number of general radiation absorbers. To block alpha/beta/gamma radiation you need pure density- more mass per volume to slow down high energy particles. You can use heavy atoms like lead or uranium, or very densely packed lighter atoms. Neutron radiation is different- the actual number of atoms per volume is critical to maximizing the number of scattering events. That means you use things like polymers- hydrocarbons, so you have as many small atoms (hydrogen) in a volume as possible. Water is one of the denser liquids, while still being 11% hydrogen by mass, vs 14% for pure polyethylene. That makes it quite good.
Even sound isn't great underwater, relatively speaking- being a fluid in motion, there's a constantly-changing distortion on everything. The thermal conductivity also means thermal signatures spread out quickly.