The short answer to your question is “all authority in heaven and on earth.” Why? After he rose from the dead, Jesus told his apostles, “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations. . . teaching them to observe all that I have commanded you.” (Matt 28:18-20).
Since some of God’s commandments involve sex, and Christ ordered his Church to teach all that he commands, the Church has the duty and authority to pass on to us what God has revealed about sexual morality. Scripture is clear that Jesus instituted his Church with such a mission. It would be unfaithful to Christ if it did not fulfill this aspect of its calling.
However, your question is really asking, “What authority does the Church have in my life at all?” Consider some of the ways Jesus made it clear that he was investing the Church with his authority. In commissioning individuals to go and preach his message, Jesus emphasized: “He who hears you hears me, and he who rejects you rejects me” (Luke 10:16). At the Last Supper Jesus told the apostles that he was conferring a kingdom upon them (Luke 22:29). He previously had promised them that whatever they “bind on earth shall be bound in heaven, and whatever [they] loose on earth shall be loosed in heaven” (Matt. 18:18).
Jesus stated that the gates of hell would not prevail against this one Church (Matt. 16:18), which was to be the pillar and foundation of truth (1 Tim. 3:15). He invested the Church with his own teaching authority because he knew that he would not be with the apostles on earth forever. He established a Church with “bishops” who “give instruction in sound doctrine” (Titus 1:7, 9). The faithful are to submit to these spiritual leaders and defer to their authority in order not to be led away by strange and diverse teachings (Heb. 13:17).
The authority of the apostles has been passed on to bishops from age to age through prayer accompanied by the imposition of hands (Deut. 34:9; 1 Tim. 4:14; 2 Tim. 1:6). Through the bishops of the Church, we are able to trace this “laying on of hands” in an unbroken line back to the apostles.
The Holy Spirit guides the Church (John 16:13) so that it teaches what God entrusted to it. The Church guards its children as a mother watches over her young. The children may not always understand the mother’s reasons for her rules, but they would do well to trust that her commands come from a loving heart and not a dictator’s whims.