Genesis 18:19-22 meaning

God reveals His plans to Abraham because He chose Abraham. Here the Hebrew word "yada" is translated as the word chosen. It means "to know," as in to know people by a relationship or by experience (Genesis 29:5, Exodus 1:8, 33:12, Nehemiah 9:7, Amos 3:2, Hosea 13:5). In other words, God was saying, "I have known him." God had entered into a deep, intimate, daily, and personal relationship with Abraham. "Yada" can also mean to know someone in an intimate way like a spouse in a marriage relationship (Genesis 4:1, 25, Jeremiah 1:5). 

The word "command" used here is a stronger word than teach or instruct (Deuteronomy 6:6-7). It means to give an order, command, or to direct someone. God commanded Adam and Eve to eat from certain trees but not to eat from the tree of the knowledge of good and evil (Genesis 2:16, 3:17). Pharaoh ordered that all newborn Hebrew males should be drowned in the Nile river (Exodus 1:22). Here, Abraham commanded his children and his household after him to keep the way of the Lord by doing righteousness and justice. Abraham was responsible as a father to teach his children the eternal values of righteousness and justice (i.e. to keep "the way of the Lord") so that they might enjoy God's blessings (Matthew 7:12, Mark 12:31).  

Abraham was to instruct his family so that God may bring upon Abraham what He has spoken. In the previous chapter, God had made a mutual covenant between me and you. Unlike the other grants and rewards, such as God's promise to grant the Promised Land, and God's promise to make Abraham a great nation, this covenant required ongoing obedience in order to receive great blessing. (Genesis 17:1-2). 

This conditional covenant was also for Abraham's descendants. God apparently desired to give Abraham an example to pass to his children, to help them command his children and his household after him to keep the way of the Lord by doing righteousness and justice. God is about to demonstrate mightily that wickedness brings judgement. This is a lesson that can be passed down in generations.

The sin and punishment of Sodom have converted the name of the city into a permanent metaphor of human wickedness and retribution. The outcry of Sodom and Gomorrah could be explained in three ways: (1) God may be personifying Sodom and Gomorrah and saying that they are crying out to him to punish the people living within them. (2) The innocent people who were hurt by the sins of the inhabitants of Solomon and Gomorrah cry out to God for justice (Exodus 22:21-24, Genesis 4:10, Psalm 9:12-13, Isaiah 5:7). (3) The sins of the people of Sodom, which they are trying to hide, are apparent to God. God knows when man sins. 

Their sin is exceedingly grave, in fact, Sodom had become so wicked that the Lord had decided to destroy them. Based on ages provided in Genesis, it had only been 400 years since the flood. Yet men had forgotten the lesson of that cataclysmic destruction (Genesis 6:5). Sodom had the witness of God saving them from the attack of Chedorlaomer and the Kings (Genesis 14:14-16); and Lot (the righteous man) lived among them as well. Still, they chose to live their wicked ways with an arrogant disregard for justice, and without showing mercy toward those in need (Jeremiah 23:14, Ezekiel 16:49-50). By clueing in Abraham to His intent, God is creating a mighty demonstration of His judgement on wickedness, callousness and injustice.

God said He would go down…and see. God is omniscient. He doesn't have to physically visit Sodom in order to know about their sin. It seems likely in this situation He is letting Abraham know that this is somewhat like an appeal.  It is so serious that God is just making sure, double checking in such a way that Abraham can be assured that Sodom's judgment is deserved. 
The men turned away…and went toward Sodom. The men who leave Abraham and go toward Sodom are the two angels who came to Abraham's tent with the Lord (Genesis 19:1). Abraham was still standing before the Lord. The third man was the Lord himself, who stays behind to talk with Abraham.