I've read here about origins of in- and un- negative prefixes. Are there any known origins of other negative prefixes such as il-, ir-, dis-, a-?
The prefix in- can be assimilated: il- before an l; im- before b, m or p; ir- before r.
The prefix dis- is of Latin origin, where it had a privative, negative, or reversing force.
a- is the trickier of all, because it has many origins and variants (I learnt a lot reading the answers to the question linked). In the sense of “not” or “without”, a- comes from the Greek, where it had the same meaning.
In English, a lot of words that mean somewhat of the same thing came about because they are from different roots. For example, Latin and German have contributed to the English vocabulary. The prefixes you mentioned have different etymologies as well. From the Oxford English Dictionary:
In English, it is now used in the following way:
In English, un- is from Old English, and is used most often when new words are created.
So why have more than one? Because English is funny that way. All three prefixes were maintained over time, and are used to combine with different sets of words. So while un and in are similar, the latter is from Latin and the former is from Old English. For a bit more information on the difference, this article from World Wide Words notes:
As reported from the NOAD
A- can also be a variant spelling of ad-, in words like ascend, aspire, and astringent.
The Greek a- prefix becomes an- before vowels, including aspirated vowels. Originally this was only used with words of Greek origin, but eventually it got used on things that came from Latin or French as well.
For example: aniconic, anovulation, aneroid, anorchism, anencephalous, anaesthesia, anangular, anallagmatic, anovulation, anorchidism, anoetic, anecdote, anonymous, anaemic, anarchy, anucleate, analphabetic, anhedonia, anaerobic, anodyne, anelectric, anhydrous, anaitiological, anhidrosis, anidiomatic, anorexia, and anantherous.
Calling someone an anorch[-id-]istic wonder just might stun him long enough for you to get away. :)
However, there is also a Greek prefix ana-, which means up to or back, and a combining form andro- meaning man or male. There’s also the an-, as in annihilate, that comes from Latin ad, so not too far from Greek ana-.