Put a Dutch oven or other heavy pot on the stove, over high heat, and review your ventilation for adequacy. Add enough oil to cover the pan bottom like a layer of felt, enough to slosh but not splash–rendering chicken skin will add more fat as you cook.
When oil is hot, brown chicken pieces in batches. A splatter guard comes in handy. Patience and leaving an inch between pot occupants will reward you with browned bird. Remove browned chicken to plate, and lower heat.
Leave fat in pot. If using dried chiles, remove seeds and stems, tear them open so they’ll lay flat, and toast them in the fat, till puffy and floppy, 3-5 minutes, then remove to chicken plate.
Add onions, tomatillos or green cherry tomatoes, and fresh tomatoes if using. Cook, turning every 5 minutes or so, until brown and blistered, about 12-15 minutes.
Add vinegar, oregano, and tomato sauce if using, add enough water to cover, bring to a boil, and reduce heat to simmer.
Cook for 90 minutes or more, until chicken easily separates from bone. Stir occasionally. If liquid level drops to expose meat, add enough water to cover.
Let cool, then put two bowls next to pot. Remove chicken and separate meat from other things.
Return chicken meat to pot, warm to serving temperature, and add fish sauce or other salt to taste. Serve on tortillas, rice, grains, or crushed tortilla chips.