Is it permissible to harm someone who caused me to be fired from my job and wronged me without my knowledge, and is it permissible for me to seek revenge on him?

The colleague who slandered and harmed you has a bad character and committed a great sin, for Allah the Almighty says: "And those who harm believing men and believing women for [something] other than what they have earned have certainly borne slander and manifest sin." It is not permissible to respond to his injustice with a similar act of disobedience, because disobedience is not countered by disobedience. The oppressed is permitted to supplicate against the oppressor to the extent of his oppression, but forgiveness and pardoning are better and more beneficial in the Hereafter, more beloved to Allah, and increase a Muslim in honor, for the Prophet (peace be upon him) said: "And Allah does not increase a servant who pardons except in honor." Furthermore, it is a way to attain Allah's pardon and forgiveness, for Allah the Almighty says: "And let them pardon and overlook. Would you not like that Allah should forgive you? And Allah is Forgiving and Merciful."