Most of the allusions are biblical in nature. Take for example what Elizabeth says about Abigail's power in the town after the accusations are starting. In act two, Elizabeth states, "Abigail brings the other girls into the court, and where she walks the crowds will part like the sea for Israel." This is referring to Moses, who parted the seas of Israel for the Israelites to escape from the Pharoah's armies. So, it indicates that Abby holds some sort of god-like power of redemption for the town. Another allusion to the bible is when John Proctor is trying to help Mary gather courage to confess to the courts that the girls are faking. In act three he bolsters her saying, "Now remember what the angel Raphael said to the boy Tobias...'Do that which is good, and no harm shall come to thee.'" He refers to that quote to help her to have strength to do what is right. Reverend Hale alludes biblically to Satan, and how "until an hour before the Devil fell, God thought him beautiful in Heaven." He is speaking of how it is possible that Rebecca Nurse could be charged with witchcraft in act two.
Because of the Puritan beliefs that the bible is all, the people were very familiar with its stories and morals, and that is probably why Miller chose to it as the main source of most of the allusions in the play. I hope that helps!