In heavy saucepan, heat oil over medium heat; cook onion and garlic, stirring until softened, about 5 minutes. Add tomatoes, crushing with fork, and tomato paste.
Drain clams, pouring juice into saucepan; set clams aside. Stir in oregano and hot pepper flakes; bring to boil. Reduce heat and simmer until thickened, about 30 minutes. Add clams, parsley, and salt and pepper to taste. Heat through; toss with pasta. Sprinkle with Parmesan.