Rinse the chicken pieces and pat dry. Mix the oregano and paprika with some salt and pepper in a small bowl. Rub the spice mixture all over the chicken and set aside for 1 to 2 minutes
Heat the oil in a paella pan or wide shallow skillet over medium-high heat. When the oil is beginning to smoke, add the chorizo and cook until the oil is a vibrant red color. Remove the chorizo to a paper towel-lined platter, then add the chicken, skin side down, and brown all over, turning with tongs. Remove the chicken to the platter with the chorizo.
Return the pan to the stove and lower the heat to medium. Now make a sofrito by sauteing the garlic and onion in the oil that remains in the pan for 7 to 10 minutes, until they begin to brown. Add the tomatoes and cook it all down until the mixture caramelizes a bit and the flavors meld. Season with salt and pepper. Combine saffron with 3 cups warm water or stock and let steep for a few minutes. Add the saffron water to the tomato mixture. Fold the rice into the sofrito, stirring to coat the grains. Add the reserved chicken and chorizo, then the clams. Simmer for about 10 minutes.
Add the shrimp and lobster (cut side down). Give the paella a couple of good stirs to tuck in all the pieces, then just let it simmer, without stirring, until the rice is al dente, about 15 minutes. Scatter the peas on top and continue to cook for 5 more minutes, until the paella looks fluffy and moist. (The ideal paella has a toasted rice bottom called socarrat.) Then let it rest off the heat for 5 minutes. Garnish with parsley and serve with lemon wedges.