Society of Jesus, is the Religious Order better know as The Jesuits. Their main function is to teach the true Catholic Faith, and in addition to the 3 usual vows of Obedience, Poverty and Chastity, the Jesuits take also the vow of Fidelity to the Pope.
Inquisition, means investigation or search. It was supposed to investigate and correct errors in the preaching and practices of the Catholic Faith. (In some places, like Spain, the "investigation" was taken to extremes, and in France the inquisitors martired St. Joan of Arc who they considered labeled a heretic).