In a large Dutch oven, heat oil over medium-high heat. Add flour, and cook, stirring constantly, until a light brown roux forms, about 3 minutes. Add onion, and cook, stirring often, until tender, about 5 minutes.
In a medium bowl, combine milk and reserved oyster liquor. Reduce heat to medium. Gradually add milk mixture to onion mixture, stirring constantly. Mixture will thicken slightly. Bring mixture to a low boil. Reduce heat to medium low, and simmer 2 minutes.
Add oysters, parsley, butter, salt, and pepper. Simmer mixture until oyster edges begin to curl, 3 to 5 minutes. Remove from heat. Garnish with green onion and celery leaves, if desired. Serve warm with oyster crackers or French bread, if desired.
* 4 (8-ounce) cans oysters, liquid drained and reserved may be substituted for the freshly shucked oysters