The oath that is obligatory to fulfil is the one which is preceded by the permission of the father. If the son made the oath without informing his father or getting his permission, it is not obligatory to fulfil it.
Try to dispose of the mud in running water or place it in the garden or the like.
It is not obligatory on the son to pay money to his father to support him financially. He is obligated to provide sustenance to his father when the latter needs it. This can be done without actually giving him the money.
If a believer receives money that is taken from a government organization, and it is known that the money had once belonged to a Muslim, it is still regarded as being owned by him. One can take this money by intending to take it on behalf of the Marja, and then he can assume ownership of it. It is better to help the needy believers with some part of it.