Perhaps the most extreme cases were the US cruisers blown apart in the night battles off Guadalcanal and neighboring islands. Ships like New Orleans and Minneapolis had their bows cut off by torpedo strikes, were saved by excellent damage control, fitted with false bows and steamed back to Pearl Harbor/US west coast for repairs. Also the Franklin was wrecked by kamikazes and fighters but managed to steam home under her own power at 14 knots. US damage control was generally outstanding; there are numerous cases of US ships being saved after taking what should have been fatal damage. Whether or not these fit the example of HoI ships steaming with 1%-5% strength remaining depends, I think, on whether you base that figure on combat strength or absolute ability to float.
Raising ships from the harbor bottom is hard work - the US BBs sunk at Pearl Harbor were tough to raise from shallow water but the capsized Oklahoma took years to right, raise and move - and the ship was effectively destroyed by the stresses of rolling over twice. Once capsized, a ship is a almost always a total loss. One feat of salvage that excited the world's admiration was the raising of the Italian battleship Leonardo Da Vinci, capsized and sunk by a magazine explosion in 1916 while loading ammunition. The Italians hoped to repair her but it would have been prohibitively expensive.
So ships can be salvaged, repaired and returned to service but this is usually done only if the damage is minor and the water shallow (as at Pearl Harbor, Alexandria and Taranto), otherwise the best course is to remove equipment and fittings and cut up the hulk for scrap. Some, of course, are left in situ as war graves.
