Curious to learn more about Ms. Hess' answer, I undertook a little more research* today...

The history begins, as with so many curiosities in the English language, with the Norman invasion in 1066. At that time, English was the language of the ordinary people, and the law. At first, William the Conqueror interfered little with use of English in official documents, primarily to bolster his claim to the throne, as it was before his reign strongly associated with the crown and kingly continuity. As time went on, however, and as more and more Normans gained positions of prominence in the English court, and were elevated to the nobility, French came to be the spoken language of the upper-class, and Latin, the imported written language of the learned, eventually came to completely replace Old English in legal documents. This continued for some 250 odd years.

By 1275, we find the first statutes written in French, and by 1310 French had overtaken Latin as the language of law. Well, not exactly overtaken; important Latin legal terms, terms of art, were being sprinkled in French language, where needed. We have inherited these terms up to the present day; this is where our civil law gets important concepts like mens rea, habeaus corpus, writs of mandamus, and a million other terms. Still, Law French was the language that lawyers communicated with each other in, and lawyers continued to develop their the profession with it, creating ever new terms of art when trying, pleading, and judging cases. Things continued in this way for a 100 more years.

Curiously, just as French was just reaching its supremacy as official written language of the Law, it was dying out as a spoken language among the nobility. Increasingly, they were speaking a bastardized pidgin of English and French called Anglo-Norman, and by 1400, Anglo-Norman had nearly died out even amongst the royal household in favor of English. Henry V broke things off completely with his Norman heritage after famously going to war with France in the Hundreds Years' War. English, with modifications, had now become the language of all the English people.

Well, mostly. Law French was still the obscure, technical language of the legal profession, and it was contributing many terms of art of its own, particularly in property law: this is where property law jargon like estoppel, estate, and esquire come from. However, even the lawyers eventually lost control of a tongue they didn't speak, and legalese became a complex argot of Law Latin and Law French terms swimming in a sea of ordinary English.

A conundrum. By 1362, we have evidence that the courts were becoming recognizant of this troublesome state of affairs, as a Statute of Pleading was enacted "condemning French as 'much unknown in said Realm'" and requiring that "all pleas be 'pleaded, shewed, defended, answered, and debated, and judged in the English tongue.'" Ironically enough, the Statute itself was written in Law French, and it was not till 200 years later, when the vocabulary of Law French had shrunk to about 1000 words, that English became the dominant language of the law.

Still, all those terms of art couldn't be simply abandoned. So lawyers of the day simply did the next best thing: they imported synonyms acknowledged as "English" to accompany those technical terms, to give the "synonyms" independent legal weight in documents, and eventually, the combination of the two became phrases with inertia of their own. Such as:

breaking and entering
fit and proper
will and testament
free and clear
acknowledge and confess
law and order
to have and to hold

(English terms are italicized.)

"But Billare!" "Isn't your answer supposed to be talking about null and void?" "And, if I'm not mistaken, doesn't null come from the Latin nullus, meaning 'not any, none,' and doesn't void come from the Latin vocivus, meaning 'unoccupied, vacant'"? "Where's the Old English term there?!"

Ah, yes. The punchline. Null and void became a phrase of their own because the two synonyms from Latin were imported at different times into "ordinary" English. I quote from David Melinkoff's The Language of Law:

Early in the reign of Elizabeth I, null – with a long life as a negative in law French and in Latin – became an English synonym for the law's use of void. Another hundred years, and null and void were a team, null taking the place of other explanatory nothingness (no value, no effect) that had often accompanied void. The combination stuck despite frowns in and out of the law.

So it follows the same rule. Null and void is a semantically redundant phrase because it was formed as a compromised term of art, and has continued in this way for a long, long time.

*: All acknowledgments and quotes go to this most excellent book, Legal Language, by a certain Peter Tiersma, where I found basically most of this research. Do read it if you're interested in more.