The Moon and Sun don't just stretch the oceans; they stretch solid Earth too. Through these Earth tides, the ground rises and falls by several tens of centimetres twice a day, and you never notice because everything moves together. The effect is real enough that CERN physicists had to account for it: it changed the 27 km circumference of their accelerator by about a millimetre.
On 27 August 1883, the eruption of the Indonesian volcano Krakatoa was heard as far away as Rodrigues Island, nearly 4,800 km away. Its pressure wave was picked up by barometers worldwide and circled the globe several times. The tsunamis that followed killed more than 36,000 people.
The deepest known point in the ocean, Challenger Deep, lies roughly 10,900 m below the Pacific surface. Drop Everest in and its summit would still sit about 2 km underwater. Down there, the pressure is more than 1,000 times what you feel at sea level, roughly a tonne pressing on every square centimetre.