Heat olive oil over medium-high heat in a large stockpot. Cook and stir onions in the hot oil for 5 minutes. Add celery, carrots, and bell peppers and saute for an additional 5 minutes. Stir in cilantro, oregano, and bay leaves. Saute for 2 minutes more. Add water, fish parts, fish heads, clam juice, and peppercorns.

Bring mixture to a boil, reduce heat to low, and let simmer, uncovered, for at least 4 hours. Turn off heat and let cool for about 30 minutes.

Remove bulk items from stock using a skimmer or slotted spoon. Strain stock through a fine-mesh strainer into a large container, making sure all fish bones have been removed. Use or freeze for future use.