Combine the oil, soy sauce, vinegar, lemon juice, Worcestershire sauce, honey, dry mustard, parsley, black pepper and garlic in a medium bowl. Mix well.
Trim the tenderloins of any extra fat and silver skin and add to a sealable plastic bag and place on a shallow dish.
Pour the marinade into the bag over the meat; close the bag.
Refrigerate tenderloins overnight, or at least 8 hours, turning the bag occasionally to redistribute the marinade.
When ready to cook, heat a gas grill to high until the grill is fully heated, about 15 minutes.
Drain the tenderloins and pat dry.
Take a few paper towels and fold them several times to make a square. Blot a small amount of oil on the paper towel and carefully wipe the hot grates of the grill to make a non-stick surface.
Place the pork on the hot grill grates.
Close the lid and grill for 7 minutes.
Turn the pork over, close the grill and cook for another 6 minutes.
Turn off the heat (keep the lid closed) and continue to cook the pork for another 5 minutes.
Insert an instant-read thermometer into the middle of the thickest end of the tenderloin. The thermometer should read 145º to 150ºF. If not, close the lid and let the pork continue to roast in the residual grill heat.
Allow to rest for 5 to 10 minutes before slicing to serve.