Mash garlic, oregano, and 1 teaspoon salt together in a bowl.

Douse chicken, beef, and pork with lemon juice in a large bowl. Drain half the liquid. Mix the mashed garlic, half of the onions, 2 tablespoons vegetable oil, and vinegar into the meat mixture.

Heat the remaining 1/2 cup vegetable oil in a large skillet over medium-high heat. Add the meat mixture in batches and cook until browned on all sides, 15 to 20 minutes.

Transfer the browned meats into a large pot. Add half of the water, chicken broth, beef consomme, 2 bouillon cubes, and 1 teaspoon salt. Bring to a boil; reduce heat to low and simmer, covered, until meats are more than halfway cooked through, about 40 minutes.

Combine pumpkin, sweet potatoes, eddeos, yuca, potatoes, plantains, corn, celery, carrots, green pepper, cilantro, and adobo seasoning in the simmering pot. Return soup to a boil. Reduce heat to low and continue simmering until the sancocho is thick and the root vegetables are soft, 1 to 2 hours. Stir in the remaining half of the water by gradual increments to replace any evaporated liquid.