Yes garlic oil does need to be refrigerated.
Do not leave garlic oil or garlic in oil at room temperature longer than an hour or two because bacteria can grow in the garlic oil and make you sick.
Garlic oil must always be kept refrigerated to prevent bacteria from growing in it and prevent the garlic oil from going bad.
If you leave garlic oil out for longer than a few hours it should be thrown out because it can cause you to get sick if you use the garlic oil that is left out longer than a few hours.
Garlic oil will last for up to 4 days in the refrigerator and for a few months in the freezer.
If the garlic oil has been in the refrigerator longer than 4 days then it's likely no good anymore and should be thrown out.