Q?

Could you list all the levels of Church authority and an example of a teaching in each level?

A!

Thanks for the great question. After some research, I found two places that go a long way toward answering the question. I don't have the book you referenced, but the information below is very comprehensive. The second source actually names and gives examples of papal teaching types.

July 1990 This Rock Magazine:
A: Jesus commanded his apostles to teach his gospel to all nations until the end of time (Matt. 28:19-20). The magisterium of the Church refers to the teaching authority he gave to his apostles and through them to their successors, the bishops of the Church united with the Pope, the successor of Peter.

The ordinary magisterium refers to the normal manner by which the bishops instruct the faithful--the daily preaching of the gospel, their oversight of the catechetical formation in their dioceses, the issuance of pastoral letters, developing diocesan guidelines on prayer and worship, and so on.

Not everything taught by the ordinary magisterium of the Church is infallible--absolutely free from even the possibility of error due to the Holy Spirit's safeguard--but much is. On this point, Vatican II's Dogmatic Constitution on the Church states:

"Although the bishops, taken individually, do not enjoy the privilege of infallibility, they do, however, proclaim infallibly the doctrine of Christ on the following conditions: namely, when, even though dispersed throughout the world but preserving for all that among themselves and with Peter's successor the bond of communion, in their authoritative teaching concerning matters of faith and morals, they are in agreement that a particular teaching is to be held definitively and absolutely" (Lumen Gentium, no. 25).

The extraordinary magisterium of the Church can also teach infallibly. There are two forms of the extraordinary magisterium.

First, there's the teaching of an ecumenical council. We've had 21 of them in the history of the Church, the most recent being Vatican II. This form of magisterial teaching occurs when the bishops of the Church assembled in council, with the pope as the head of the episcopal college, define a teaching on matters of faith and morals. In such circumstances their teaching is infallible.

The second form of the extraordinary magisterium is an ex cathedra pronouncement from the pope. This is papal infallibility. Vatican II described papal infallibility this way:

"The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful--who confirms his brethren in the faith (cf. Luke 22:32)--he proclaims in an absolute decision a doctrine pertaining to faith and morals.

"For that reason his definitions are rightly said to be irreformable by their very nature and not by reason of the assent of the Church, inasmuch as they were made with the assistance of the Holy Spirit promised to him in the person of blessed Peter himself" (Lumen Gentium, no. 25).

In addition to infallible teaching by the magisterium, there's also what is often called "authentic teaching," teaching which hasn't been presented infallibly by the ordinary or extraordinary magisterium, but which is still authoritative and to be accepted by Catholics.

In speaking of "authentic teaching," Vatican II declared:

"Bishops teaching in communion with the Roman Pontiff are to be respected by all as witnesses to divine and Catholic truth. When their bishop speaks in the name of Christ in matters of faith and morals, the faithful are to accept his teaching with a religious assent of soul.

"This religious submission of will and of mind must be shown in a special way to the authentic magisterium of the Roman Pontiff even when he is not speaking ex cathedra. That is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence and the judgments made by him are sincerely adhered to, according to his manifest mind and will" (Lumen Gentium, no. 25).

New Advent "Catholic Encyclopedia"
In official language papal documents have at all times been called by various names, more or less descriptive of their character. For example, there are "constitutions," i.e., decisions addressed to all the faithful and determining some matter of faith or discipline; "encyclicals," which are letters sent to all the bishops of Christendom, or at least to all those in one particular country, and intended to guide them in their relations with their flocks; "decrees," pronouncements on points affecting the general welfare of the Church; "decretals" (epistolae decretales), which are papal replies to some particular difficulty submitted to the Holy See, but having the force of precedents to rule on all analogous cases. "Rescript," again, is a form applicable to almost any form of Apostolic letter which has been elicited by some previous appeal, while the nature of a "privilege" speaks for itself. But all these, down to the fifteenth century, seem to have been expedited by the papal chancery in the shape of bulls authenticated with leaden seals, and it is common enough to apply the term bull even to those very early papal letters of which we know little more than the substance, independently of the forms under which they were issued.