Drain the oysters through a fine-mesh sieve placed over a small bowl to catch the oyster liquor. Set the oysters aside. Reserve the liquor.
In a medium saucepan, melt the butter over medium heat. Stir in the Worcestershire sauce, paprika, and celery salt. Add the oysters and bring to a simmer. Cook just until the edges of the oysters curl.
Add the oyster liquor to the pan and return to a simmer. Add the milk, cream, and nutmeg and reduce the heat to low. Cook, stirring occasionally, until heated through, but do not let the oyster stew boil. Season to taste with salt and pepper.
Ladle the oyster stew into a warmed tureen or individual bowls, garnish with the parsley, and serve hot.