What is the Shar'i ruling on Amjad's oath and on the stolen money he took from Salem, knowing that he is remorseful and does not know the whereabouts of the original owner of the money? And what is the expiation for both?

Stolen money is not permissible to keep or to benefit from. The way to dispose of it after repentance is to return it to its owner or their heirs. If it is impossible to deliver it to them, then it should be given as charity with the intention that the reward goes to its owner. As for the profits of invested stolen money, these belong to the investor, not to the owner of the money. Regarding the oath: if Amjad swore that Salim does not deserve the stolen money, and his intention was that it is not rightfully his, then this intention is correct. However, if he swore to take the money, then this is a false oath (yamin ghamus), which is one of the major sins, and sincere repentance is obligatory for it.