This is a very good question and one very difficult to answer. I’ve worked as a legal proofreader for many years, and whilst (I think ;-)) I know when to use one and not another, I have never considered what the exact differences in meaning are. Also, be aware that even lawyers are not always clear as to their exact legal meanings outside the lawyers' areas of expertise or jurisdiction. Anyway, with that qualification, I will do my best to explain what I think the differences and similarities are in meaning. (If anybody wants to add, clarify or challenge anything I’d be more than happy because I’d like to finally nail these definitions for my own benefit!)
(The definitions below and certain quotes are taken from the Oxford English Dictionary (OED) and the Modern Guide to Synonyms and Related Words by S.I. Hayakawa (HAY).)
Annul
declare invalid (an official agreement, decision or result) (OED)
the elections were annulled by the general amid renewed protests
declare (a marriage) to have had no legal existence (OED)
her first marriage was finally annulled by His Holiness
end something existing or declare that it never really existed (HAY)
(a) If a contract (eg a business agreement or marriage contract) is annulled it is considered to have never existed so the parties are returned to the position they were in before they entered into the contract. Contrast with ‘terminate/cancel an agreement’ where the agreement has no retroactive effect – its effect ends only upon the date of termination/cancellation
(b) The individual or entity that annuls a contract must have legal capacity to do so – you yourself cannot annul a contract. In democracies, this would generally mean a legislative body, such as a court, but see the first example above where the general annuls the elections (ie declares the results of the election to be invalid, as if the elections had never happened). The fact that the general was able to do this suggests that the reference is not to a democracy but to a military dictatorship where the military has legal authority to act.
(c) This is a legal term and most people are only familiar with its meaning in the context of declaring a marriage contract void. Note the difference between ‘annul a marriage’ and ‘declare a marriage to be at an end’ – with annulment, you are considered never to have married; whereas ‘declaring …’ means the marriage has ended in divorce.
Rescind
revoke, cancel or repeal (a law, order or agreement) (OED)
The government eventually rescinded the directive
Bring to an end the effect of an order and by depriving it or the authority behind it, invalidate it (HAY)
When issuing new regulations, a military headquarters may rescind earlier regulations governing the same subject
(a) As with (a) under ‘annul’, if a law, order or agreement is rescinded, it is declared null and void and the position before it came into effect is restored.
(b) ‘rescind’ is often used where a body (or individual) cancels out an earlier action taken (i) by that body, (ii) by another body with equivalent status or (iii) by another body under the rescinding body’s authority – unlike ‘annul’, the rescinding body need not have legislative capacity. So:
- a government might pass a law and then later rescind that law;
- a general may give an order then later rescind that order;
- a referee may issue a red card to a football player and then the Football Authority, under whose authority the referee falls, may rescind that red card;
- two parties might enter into an agreement then by mutual consent later rescind that agreement; and
- you might make a promise then later rescind that promise,
in each case as if there had never been such law, order, red card, agreement or promise.
(c) Outside its legal use, ‘rescind’ is a very formal word and not often used. A government might instead ‘overturn’ [edit: 'repeal' is correct here - see how difficult it is!] an earlier law, a general ‘reverse’ his order, the FA ‘overturn’ the red card, the two parties ‘declare null and void’ the agreement and you ‘withdraw’ an earlier promise.
Nullify
make legally null and void; invalidate (OED)
Judges were unwilling to nullify government decisions
The provisions of The Companies Act 2006 on auditor’s liability revised and in some cases nullified the earlier provisions under The Companies Act 1985
make of no use or value; cancel out (OED)
Insulin can block the release of the hormone and thereby nullify the effects of training
Prevent or end the effectiveness of some condition or activity. Often it means to counterpose an action or a condition that renders the original action of condition futile or inoperative (HAY)
Counter-intelligence seeks to nullify the enemy’s espionage efforts
The overriding sense is that one thing cancels out the effect of another completely. Where A nullifies B, A could exist before B has effect (insulin [A] already in the body can nullify the effects of training or after B has effect (it was only 21 years after The Companies Act 1985 that it was superseded - another word to know, used where one law takes over from an earlier law - by The Companies Act 2006 [A] and during that time the earlier act had effect), so unlike ‘annul’ and ‘rescind’ the effect is not retroactive – A nullifies B from the point where the 2 co-exist.
Revoke
put an end to the validity or operation of (a decree, decision or promise) (OED)
The men appealed and the sentence was revoked
If you drink and drive your licence will be revoked
Pop Star Lily Allen has had her visa revoked
Bring to an end something that has been authoritatively given, permitted or granted (HAY)
King Louis XIV revoked the Edict of Nantes, in which King Henry IV had granted religious liberties to the French Huguenots
Similarly to rescind, the sense is that a body (or individual) takes back the earlier decree, decision or promise of (a) that same body, (b) another body with equivalent status or (c) another body under the revoking body’s authority. So, in the examples above:
-the sentence was handed down by a court and later revoked by either the same court, a court with equivalent status or a more senior court (‘overturn’ is a more commonly used word in this sense but I think it is used more often where the first court’s decision is reversed before it has come into full effect – for example, if you are ordered to pay damages by a district court and then appeal to a more senior court, which overturns the decision of the district court, so that you actually pay no damages);
-the body that issued your driving licence is the one that will revoke your driving licence if you drink and drive; and
-the government department that issued the visa cancelled that visa.
Finally, two points to bear in mind:
(a) Depending on the context, these words can be quite formal – ‘cancel’, ‘cancel out’, ‘withdraw’, ‘take back’, ‘take away’, ‘overturn’ and many others are more common
(b) Clearly from the above definitions/examples, there is some overlap in meaning, even without bringing up other related words such as ‘repeal’ and ‘abrogate’. Sometimes more than one word can be used; at other times, eg ‘annul a marriage’, there is only one preferred option and confidence in choosing which of the (near) synonyms to use will grow the more you see them used in context.