Heat
Temperature in the ocean is primarily controlled by the absorption of sunlight. 99% of light is absorbed in the upper 100 meters of the oceans. Here is a typical temperature profile. Note the pronounced thermocline at about 100 meters.

Salinity
Salinity varies with depth in the ocean, but it is very different from region to region. In rainy regions, surface water will be diluted by the fresh water in rain, so the surface water will have a lower salinity than deep water. In arid regions, evaporation of surface water makes the water left behind more salty than the underlying water. Therefore, the halocline can go either from high salinity to low salinity, or the other way around, or it may not exist at all.
Density
Density is primarily controlled by temperature and salinity. Warm water is less dense than cold, and salty water is more dense than fresh. Because temperature varies more than salinity, there is usually a strong pycnocline at the same depth as the thermocline. The pycnocline provides a barrier to mixing of surface and deep water.

Dissolution
Calcium carbonate dissolves better in colder water, in acidic water, and at higher pressures. In the deep ocean, all three of these conditions exist. Therefore, the dissolution rate of calcium carbonate increases greatly below the thermocline. This change in dissolution rate is called the lysocline.
Below the lysocline, more and more calcium carbonate dissolves, until eventually, there is none left. The depth below which all calcium carbonate is dissolved is called the carbonate compensation depth or CCD.
Pressure
Pressure has no "cline." Pressure increases gradually the deeper you go in the ocean, so pressure is a linear function of depth.
Sound velocity
Sound velocity depends on two factors. Sound travels faster through water at higher pressures and at warmer temperatures. So, sound velocity decreases as you descend below the thermocline. As you go deeper, though, pressure increases, and the sound speed gets higher again. This creates a zone of minimum sound velocity right near the thermocline. All sounds emitted near this minimum sound speed layer (called the SOFAR channel) tend to get trapped inside. This focuses the sounds, and they can travel great distances. The SOFAR channel is used by ships, scientists, and whales to transmit sound around the ocean.