In general, ingredients that do not require refrigeration alone do not require it together. If you use EVOO as your oil, then it will solidify at refrigerator temperatures, too, requiring you to set it out ahead of time so it can be used. A dressing with nothing in it but the ingredients you list could be kept in the pantry, assuming they and their mixture all are clean.
If you put cheese or garlic in it, however, keep it chilled. At room temperature the cheese will go rancid much more quickly than the oil, and garlic frequently carries botulism which grows in the airless environment of a dressing but is slowed by refrigeration.