Combine the white vinegar, canola oil, sugar, white pepper, garlic salt, oregano leaves, white wine, and mustard in a glass mixing bowl. Blend mixture well.
Place cleaned mushroom caps into a pyrex baking pan, and then pour the marinade over the top of the mushroom caps.
Cover with lid, or Saran wrap.
Refrigerate the mushrooms in the marinade overnight. When ready to serve, stick each mushroom cap with a toothpick.