Place hake in a deep dish and sprinkle generously with 3 tablespoons salt. Cover with plastic wrap and refrigerate until salt is absorbed, 2 to 3 days.
Whisk oil, vinegar, salt, and black pepper together in a bowl. Add onion; mix well to combine. Let marinate in the refrigerator until serving.
Rinse hake with cold water and place in a large pot. Pour in water to nearly cover; bring to a boil. Reduce heat and simmer until easily flaked with a fork, about 20 minutes. Remove from water and transfer to serving plates.
Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain and divide among serving plates.
Heat a skillet over medium heat; fry salt pork until lightly browned and crisp, about 5 minutes.
Mash hake and potatoes together with a fork. Mix in slices of crispy salt pork and spoonfuls of fat from the skillet. Top with a few sliced onions and serve.