The LDS Church has consistantly taught that one cannot perform an ordinance which the person has not received himself. Yet Joseph and Oliver baptised each other before receiving the ordinance of baptism themselves. This seems out of order. Can you enlighten me?
Performing a Priesthood ordinance requires two elements: Priesthood authority and the Priesthood keys for that ordinance. As I mentioned in a previous answer, Joseph and Oliver were given the Aaronic Priesthood authority by the resurrected John the Baptist, who also held the keys to the ordinance of baptism and bestowed those keys on them.
The practice of bestowing a Priesthood office or saving ordinance by someone who has himself not yet received the ordinance is occasionally found early in a dispensation of the gospel, when such ordinances are being restored. For example, the Book of Mormon records that Alma baptized Helam and simultaneously participated in that ordinance himself. Similarly, the Three Witnesses to the Book of Mormon called and ordained the original Twelve Apostles in our own dispensation, despite the fact that they themselves did not hold the Priesthood office of apostle. They had been given the responsibility and the keys to this duty, so they did not need to hold that Priesthood office themselves.
In the Church today, we see this same principle in action when a stake president, who holds the Priesthood office of high priest, calls and ordains a stake patriarch. Until fairly recently, the duty of calling and ordaining the stake patriarch was done by a member of the Quorum of Twelve Apostles, but with the growth of the Church and the great increase in the number of stakes, this duty was given to the stake president (though always with the approval of the Twelve). The stake president himself need not hold the Priesthood office of patriarch — indeed, he rarely or never does. Rather, he holds the keys to make that calling and ordination, and along with the Priesthood itself, that is all that is required.