Rinse the chicken pieces and pat dry. Season all over with salt, black pepper, and oregano. Heat the oil in a paella pan or wide skillet. Brown the chicken on all sides, when nearly cooked through, add the chorizo links and brown.
Remove the chicken and sausage from the pan. Cut the sausages into slices and set aside. Drain out excess oil but don't clean the pan. Make a sofrito by sauteing the garlic, onion, and tomatoes, cook until the mixture caramelizes a bit and the flavors meld. Season with salt, black pepper, and paprika.
Add the rice, stirring to coat the grains. Steep the saffron in 1/4-cup hot water for 5 minutes then stir it into the rice.
Add the stock/water and simmer for 10 minutes, gently moving the pan around so the rice cooks and absorbs evenly. Do not cover or constantly stir like risotto. Add the shellfish and the reserved chicken and sausage. Simmer, without stirring, until the rice is al dente and the mussels have opened. (Do not eat any mussels that do not.)
Scatter the peas on top and continue to cook until the liquid is absorbed. The ideal paella has a toasted rice bottom called socarrat. Allow to rest off the heat for 5 minutes before serving. Garnish with lemon wedges and strips of pimento.