How does the Church continue Jesus mission sacramentally and ethically?

Roman Catholic Answer:

Jesus mission was primarily to offer Himself in sacrifice, dying for our sins and repairing the great evil which had been wrought in the world through man's sin starting with "Original Sin" - that of Adam and Eve. The way He accomplished this was through the Cross on Calvary. The way He applies this to each and every person throughout history is through His Church which is His Mystical Body. He commissioned the apostles and sent them out into the world to bring men to the knowledge and love of Him. We are saved by accepting Jesus personally each moment of our lives and showing that in the way we live. The ethics of Christian morality are revealed to us by Jesus through His church and the Bible. We gain the ability and strength to do this through the sacraments which were instituted by Him and are administered by His priests through the Church. The Church IS the Mystical Body of Christ, and each and every ordained priest is an "alter Christus" - another Christ. They lend their mouths and hands to Him so that through them He can teach, feed, and lead us to heaven. No sacraments are effective until one has been baptised. The rest of the sacraments are various means of grace in which Christ comes to us to strengthen and guide us EXCEPT the Most Holy Eucharist. The Most Holy Eucharist IS Jesus Christ, Himself, present under the appearances of bread and wine. In the other sacraments, He extends grace to us through them. In the Most Holy Eucharist, He, Himself, comes to us (if we are receiving Him in a state of grace), strengthens us and guides us in life.