Heat the olive oil in a large pot over medium heat. Add the onion and cook until it softens, about 5 minutes.
Stir in the garlic and cook for 1 minute until fragrant.
Add the potatoes, olives, diced tomatoes, vegetable broth, and oregano. Bring the mixture to a boil, then lower the heat and simmer for 15 minutes until the potatoes are tender.
Gently place the cod pieces into the simmering broth. Cook for 5 to 7 minutes until the fish turns opaque and flakes easily with a fork.
Season with salt and pepper to taste. Ladle into bowls and top with parsley. Serve with lemon wedges on the side.