This topic requires a bit of knowledge on phonetics and phonology, which was initially discussed in this post about phonetics.
im-
Example words: impractical, imbalance, improper, impressive
Notice how words that take the im- negative prefix start with p and b. The p and b sounds are made with the lips, and this is the same place of articulation as the m sound. This is known as assimilation: the place of articulation of the final sound of the prefix ("m") matches the place of articulation of the initial sound of the root word.
in-
Example words: inaccessible, involuntary, insincere, infamous
In most other cases, the in- negative prefix is used. This is because n is an alveolar consonant, pronounced with the tongue against the area just above the upper teeth. Unlike the p and b sounds, this is a central area, and thus the in- prefix can "handle" many other sounds.
il-, ir-
Example words: illogical, illegal, irrational, irresponsible
The l and r sounds are known as liquids. Just like the im- prefix, assimilation happens here. In this case, the l or r is simply doubled up in forming the prefix.
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