Answer is no, oil is not soluble in water.
Reason: oils are hydrophobic, or “water fearing.” Instead of being attracted to water molecules, oil molecules are repelled by them. As a result, when you add oil to water the two don't mix with each other.
Oil does not have any polar part and so for them to dissolve in water they would have to break some of waters hydrogen bonds. Water will not do this so the oil is forced to stay separate from the water.