I cannot speak for the teaching of every denomination, but most Christians would argue that the death of Christ abrogated the ritual law but not the moral law. Saint Paul in his letters never argues that Christ changed the moral law. Instead, Jesus and the Apostles speak only of abrogating the requirements of the ritual law, including but not limited to circumcision, purification of dishes, ritual purity and cleanliness, and the prohibition on the consumption of pork and other unclean foods. The Sacrifice on the Cross also surpasses and eliminates the need for animal, cereal, and other offerings in the Temple.
Moreover, the commandments of God do not consist solely of a list of prohibited actions: we can sin in thought and word and omission too. Jesus Himself identified love of God as the greatest commandment and love of fellow humans as the second greatest. And love is difficult, not emotive, potentially sacrificial, and never selfish: Jesus provided its greatest expression with His death on the Cross that we may live eternally with Him through our faith despite our sins.
Exactly. The idea that because Jesus never specifically addressed sodomy, bestiality, necrophilia, etc. they are no longer abominations is, well, silly.