In Hinduism, it is a practice to offer oil to Shani Dev usually mustard oil. This belief has a story behind it.
According to Hindu scripture Ramayana, at the time when the bridge was constructed between Rameswaram and sri Lanka by Lord Ram’s army, Lord Hanuman took the responsibility for the security of the bridge so that enemies could not destroy it. But one day when Lord Hanuman was sitting under the tree and offering prayer to Lord Rama, God Shanidev came near him and said,” I am the most powerful God and I want to test your strength. Open your eyes and fight with me if you can.”
After hearing all this, Lord Hanuman opened his eyes and said that he is meditating upon his God and requested Shanidev not to disturb him. Since Shanidev insisted for long so Lord Hanuman replied by stretching out his tail and coiled it around Shanidev . And then Lord Hanuman hit him against the bridge due to which Shanidev started bleeding.
Shanidev could not bear the excruciating pain so he requested Lords Hanuman to stop and promised that he will never repeat this mistake again.
Later Lord Hanuman warned him that if he will ever try to hurt Ram’s devotees, he will have to face the consequences. To which Shanidev said,” I will do as you say and will not interfere in the destiny of those devoted to you and Ram.”
When Lord Hanuman allowed Shanidev to move, he asked Lord Hanuman to apply some oil to relieve the pain.
Since that time, it has been adopted as a routine to offer oil to Shanidev.
Thus offering oil symbolises soothing the pain.