The justification for "judges" in Ex. 21:7 is contextual. Those who translate it that way believe that a dispute between a master and his Hebrew slave would be taken to judicial authorities rather than God. However, it cannot be denied that bringing the matter to "God" is another possibility. For example:
Therefore Saul said, “O Lord God of Israel, why hast thou not answered thy servant this day? If this guilt is in me or in Jonathan my son, O Lord, God of Israel, give Urim; but if this guilt is in thy people Israel, give Thummim.” - 1 Samuel 14:41
A formal of judicial proceeding involving God as the decider can also be found in Numbers 5:11-31, where a man is directed to bring a possibly unfaithful wife to "stand before the Lord" and be tested.
Instances of leaders and people alike seeking to "inquire of the Lord" for his judgment are mentioned frequently in the biblical text. But translators apparently feel that this particular case doesn't rise to that level of magnitude.
However RSV and others agree with @Nihil:
When you buy a Hebrew slave, he shall serve six years, and in the seventh he shall go out free, for nothing. 3 If he comes in single, he shall go out single; if he comes in married, then his wife shall go out with him. 4 If his master gives him a wife and she bears him sons or daughters, the wife and her children shall be her master’s and he shall go out alone. 5 But if the slave plainly says, ‘I love my master, my wife, and my children; I will not go out free,’ 6 then his master shall bring him to God, and he shall bring him to the door or the doorpost; and his master shall bore his ear through with an awl; and he shall serve him for life.
The same holds for Ex. 22. Translators believe that a matter of simple theft would be decided by local authorities, not taken to God through divination, oracles etc. But once again RSV sides with @Nihil.
If the thief is not found, the owner of the house shall come near to God, to show whether or not he has put his hand to his neighbor’s goods.
The reason translators want to use "judges" rather than "God" for elohim may also be related to their theological agenda. Psalm 82 is perhaps the best example. It is a complicated issue because in the first verse, elohim appears twice, and el appears once. In that case translators dislike "God" orreject "the gods" for elohim, because it implies that other deities than Yahweh actually existed. The variety of translations for Ps. 82:1 is impressive. "Elohim" becomes both God and "the gods" as well as "judges." Two versions will suffice to illustrate the issue:
RSV God has taken his place in the divine council; in the midst of the gods he holds judgment.
ICB God is in charge of the great meeting of his people. He judges the judges.
In sum, the justification for "judges" in the verses mentioned is the context of a relatively mundane judicial proceeding. But since judicial decisions are known to have involved taking the matter to God in other passages, "God" is probably the better translation here.