Answer 1

There are a lot of examples of Apostolic Tradition. The first example is the form of worship, which is the Liturgy. We read from Justin Martyr: 

“On the day we call the day of the sun, all who dwell in the city or country gather in the same place. The memoirs of the apostles and the writings of the prophets are read, as much as time permits. When the reader has finished, he who presides over those gathered, admonishes and challenges them to imitate these beautiful things. Then we all rise together and offer prayers for ourselves . . .and for all others, wherever they may be, so that we may be found righteous by our life and actions, and faithful to the commandments, so as to obtain eternal salvation. When the prayers are concluded we exchange the kiss. Then someone brings bread and a cup of water and wine mixed together to him who presides over the brethren. He takes them and offers praise and glory to the Father of the universe, through the name of the Son and of the Holy Spirit and for a considerable time he gives thanks (in Greek: eucharistian) that we have been judged worthy of these gifts. When he has concluded the prayers and thanksgivings, all present give voice to an acclamation by saying: 'Amen.' When he who presides has given thanks and the people have responded, those whom we call deacons give to those present the "eucharisted" bread, wine and water and take them to those who are absent.” (Apology 1, 65-67)

Nowhere in the NT does it show how the form of worship will be, but it has been through early Church Fathers that we can know how they worshipped. This affects the doctrine of the Mass, which is obvious.

Another Apostolic tradition is apostolic succession. Pope Clement says:

“Our Apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned, and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry. As for these, then, who were appointed by them, or who were afterwards appointed by other illustrious men with the consent of the whole Church, and who have ministered to the flock of Christ without blame, humbly, peaceably and with dignity, and who have for many years received the commendations of all, we consider it unjust that they be removed from the ministry.” (Letter to Corinthians 44,1)

This statement shows what apostolic succession is. It also shows how apostolic succession went. Another Apostolic Tradition is to follow Apostolic Tradition.

ST. IRENAEUS OF LYONS (c. 180 AD):

“So forceful are these arguments that no one should henceforth seek the truth from ANY OTHER SOURCE since it would be simple to get it from THE CHURCH ....On this account are we bound to avoid them, but to make choice of the things pertaining to the Church with utmost diligence, and to lay hold of the TRADITION OF TRUTH ..For how should it be if the Apostles themselves had not left us writing? Would it be necessary [in that case] to follow the course of Tradition which they handed down to those whom they committed the Churches?” (Against the Heresies 3:4:1)

“Though none others know we the disposition of our salvation, than those through whom the Gospel came to us, first heralding it, then by the will of God delivering us the Scriptures, which were to be the foundation and pillar of our faith. ...But when the heretics use Scriptures, as if they were wrong and unauthoritative, and we variable, and the truth could not be extracted from them by those who were IGNORANT OF TRADITION. And when we challenge them in turn with that TRADITION, which is FROM THE APOSTLES, which is guarded by the succession of presbyters in the churches, they oppose themselves to TRADITION, saying they are wiser, not only than those presbyters but even than the Apostles! The TRADITION OF THE APOSTLES manifested, on the contrary, in the whole world, is open in every church to all who seeks the truth ...And since it is a long matter in a work like this to enumerate these successions, we will confute them by pointing to the TRADITION of the greatest and most ancient and universally-known Church founded and constituted at Rome by the two most glorious Apostles, Peter and Paul, a TRADITION which she has had and a faith which she proclaims to all men FROM THOSE APOSTLES.” (Against the Heresies 3:3:1-3)

I really do not know what Julie means by “differed.” Oral message is certainly different either by elaboration, or a different message. I do not believe that it was a different message, however, I do believe that Paul elaborated more of the teachings when he preached. One example is the form of worship. One example of writing that shows oral tradition is by the author of Second Clement, which says, For the Lord said, “You will be like lambs among wolves,” But Peter replied by saying, “What if the wolves tear the lambs to pieces?” Jesus said to Peter, “After death the lambs should not fear the wolves, nor should you fear those who kill you and can do nothing more to you. But fear him who, when you are dead, has power over soul and body to cast them into the flames of hell.” (Second Clement, 5, 2-4).

Also, Dr. Lienhard adds,

“In the period of Apostolic Fathers, it is still the words of Jesus, rather than any written Gospel, that are authoritative. When the Apostolic Fathers quote the Scriptures (and not all of them do), they almost invariably mean the Old Testament. They do not have a New Testament. But they quote the words of Jesus as authoritative seventeen times. A few passages will show an important pattern evolving. In a few cases the Apostolic Fathers quote one of the Gospels verbatim. Polycarp of Smyrna writes: “