What would happen if you submerged a stargate in the ocean and either dialed out or someone dialed in?

Immediately after dialing? the water occluded by the Kawoosh would be vaporized. After that, not much. Its pretty explicitly stated in an episode (don't remember which) that the gate's event horizon is used to filter out what does or does not pass through the gate. It effectively limits it to only solid matter with momentum, or energy, to pass through it. That's why you can have differing atmospheres, or even a gate in hard vacuum without any negative effect to the opposite side.

The episode 'Watergate' (S04E07) involves a submerged Gate. It apparently can detect the Waterpressure at the event horizont and basically block water from flooding through the wormwhole to the other side.

This hsppens in an Atlantis episode, "The Shrine," and the gate seems to work. Atlantis has the shield up, luckily, so the water from the dial-in doesn't come through from the flooded gate. The gate does not shut down normally, however, due to water continually attempting to pass through and requires the 38-minute buffer to close the connection. Once it closes, Atlantis dials back out to the flooded gate and sends a jumper through.

I don't think it'd flood, I think motion would bring some liquid in though if a physical object of enough mass pushed through. Or the gate would act as if it was buried and there wouldn't be a connection.