Wipe mushrooms with a damp cloth. In a medium saucepan, steam or cook mushrooms in boiling water for 1 minute. Drain and quickly cover with cold water; immediately drain again.
In a large bowl, combine oil, vinegar, garlic, oregano, thyme, pepper, paprika, and salt; stirring to blend. Alternatively, combine all ingredients in a quart-sized jar, and shake to combine. Stir in onion slices and drained mushrooms.
Cover and refrigerate at least 24 hours. Makes about 4 cups.