Curse, imprecation, malediction, anathema are comparable when they denote a denunciation that conveys a wish or threat of evil.
Curse (opposed to blessing) usually implies a call upon God or a supernatural power to visit punishment or disaster upon a person; in dignified use it commonly presupposes a profound sense of injury and a plea to a divine avenger for justice. No other word in this group suggests so strongly the certainty of the threatened evil.
Imprecation also implies an invocation of evil or calamity, but it often suggests as its provocation wrath rather than a sense of injury and a desire for revenge rather than for justice as its aim.
Both curse and imprecation are applied to profane swearing involving blasphemy, but, again, the latter is the weaker in its implications.
Malediction (opposed to benediction) is applied chiefly to bitter reproaches or denunciations publicly proclaimed and bringing disgrace or ignominy to their object.
Anathema basically denotes a solemn authoritative ecclesiastical ban or curse accompanied by excommunication.
In more general use the term applies to a strong or violent denunciation by one in authority or in a position to judge of something as grossly wrong, as productive of evil, or as accursed or it may be used in a much weakened sense to mean no more than a vigorous denunciation.