Why must they truly execute justice and not oppress the sojourner, the fatherless or the widow, or shed innocent blood, or go after other gods?

A series of conditional sentences describe how the people are to amend their ways so that the Lord will let them dwell in the land that I gave of old to your fathers forever. These sentences describe aspects of covenant faithfulness. 

If you truly execute justice one with another. This speaks to the totality of justice in the land, including the justice system and how the land was governed. But it went beyond this to how individuals treated each other as well. Everything was supposed to be done in terms of covenant faithfulness.¹

If you do not oppress the sojourner, the fatherless, or the widow. The Hebrew word asaq, translated as oppress, suggests extortion and gaining wealth by taking from others. The Lord had made it clear in his covenant that Israel was to be a people who showed concern and compassion to the outsider and the vulnerable (Exodus 22:21–24; Exodus 23:9; Leviticus 19:33–34; Deuteronomy 10:18, Deuteronomy 16:11, Deuteronomy 16:14; Deuteronomy 24:17–18; Deuteronomy 27:19).²

(If you do not) shed innocent blood in this place. The death penalty was part of the consequences for breaking certain aspects of the covenant, but it seems that this was being abused in the land and innocent people were being put to death. This took place during the rule of both Manasseh (2 Kings 21:16 and Jehoiakim (Jeremiah 26:23). The king was supposed to ensure that this did not happen (Jeremiah 22:3, Jeremiah 22:17). If the king failed then the whole nation became corrupt.³

If you do not go after other gods. This final clause identifies the cause of the moral failure of the people. They have broken the first three of the Ten Commandments by worshipping other gods before the Lord. They had rejected the complete sovereignty of the Lord and shared it with other gods.⁴ This has resulted in them breaking the other commandments in the way they have treated one another. They have not loved their neighbours as themselves because they have not loved the Lord with all their heart, soul, mind, and strength.

The end result of going after other gods and the moral and societal failure that followed was to their own harm. Covenant unfaithfulness leads to catastrophe.⁵