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For most 漢字 with multiple 音読み, there appears to be a fairly reasonable link
between the sounds, and fairly minor drift, such as with 聞 being モン or ブン.

Some 漢字, however, appear to have completely unrelated 読み, the prime example
being 回 with カイ and エ. If it was just that one it could be readily dismissed
as an historical accident, but the カイ/エ 読み is shared with the also visually
unrelated 会 and friends.

So the question is; what's going on here?

Update: As l'électeur points out, this might be explained by the size of
China, but if so: Why don't more 漢字 have these apparently unrelated 読み?
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kanji multiple-readings
Apparently unrelated 音読み?
In fact, it is perfectly normal that the 音{おん}読{よ}み of a 漢{かん}字{じ} seem to be
unrelated. Indeed, the 音{おん}読{よ}み of the 漢{かん}字{じ} were imported from China at
different period and from different regions.

There are three kinds of 音{おん}読{よ}み:

  * [漢{かん}音{おん}](https://ja.wikipedia.org/wiki/%E6%BC%A2%E9%9F%B3): Spread by the monks who studied in Ancient China around the 7th, 8th century.

  * [呉{ご}音{おん}](https://ja.wikipedia.org/wiki/%E5%91%89%E9%9F%B3): More ancient than the 漢{かん}音{おん}, those readings were imported from the Wu region of China. That lecture is very frequent in buddhist terms.

  * [唐{とう}音{おん}](https://ja.wikipedia.org/wiki/%E5%94%90%E9%9F%B3): Those lectures were introduced at the end of the Heian period. They are the most recent of the three. During the 室{むろ}町{まち}時{じ}代{だい} this lecture was called (唐{とう})宋{そう}音{おん}.
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Taking up the chance to talk about "Unrelated readings" because I get the
chance to talk about both Japan and China's phonologies in the past.

It's well known that even amongst 音読み, there are the types from different
Chinese regions and times.

漢音：Hanyin, from the original middle-chinese pronunciations

呉音：Wuyin from SE China (state of Wu)

唐音：Tangyin from Tang China around the late 1500s

慣用音：These are actually Japanese corruptions of Chinese readings, not used
anywhere in China. コク for 石 is one example, which was corrupted from ジャク (the
approximation of Hakka's pronunciation, `shak`)

There are others, usually taking name from the Chinese state that they
originate from.

**General sense**

When Japanese first borrowed Chinese character sounds （漢音）, Chinese had a
slightly different phonology to now. Firstly, `/h/` was `/φ/` (same sound as ふ
nowadays, which never changed). Usually, Chinese's `/x/` (pinyin: `h`) was
borrowed as `/k/`, but sometimes as `/w/`. Examples of this are 会 (ZH: `hui`
JP: `kai`, `e`) and 絵 (ZH: `hui` JP: `e`). Tones weren't borrowed at all.

They also copied more closely the `~ao` vs `~ou` distinctions in Chinese
(compare 道 and 豆 ZH: `dao`, `dou` JP: `dou`, `tou`). Japanese dictionaries
kindly list pronunciations of kanji that have changed. Dictionaries tell you
that 道's reading of どう actually used to be だう.

There are too many rules to list all of them out. Common ones are those above,
and final 〜う instead of `~ng` found in Chinese varieties (such as 同{どう} ZH:
`tong`).

Both Japanese and Chinese (taking Chinese as one language) have since changed,
but there are enough varieties of Chinese that it's usually clear to see which
language / dialect is the divergent one (like how Mandarin has no `-p`, `-t`,
`-k` final consonants anymore)

**In the purest sense**

"Unrelated" on'yomi are almost always going to be 慣用音. 良 has a fair few, such
as ら, which sound nothing like the Chinese `liang` used today. This is because
they actually diverged from the Chinese loanwords into something distinctly
Japanese, and is also why they're so uncommonly used in actual words (I can't
think of any examples of 良 as ら other than in names).

**Other reasons**

One thing to note is that sometimes the Chinese itself was unclear when Japan
borrowed the sounds, even without different languages or bad transliterations.
There are kanji that have readings with `/m/` initials, and some with `/b/`
(文聞無望亡 to list a few). These are all taken from the same Chinese regions and
time, but people probably couldn't say which it sounded more like, and use
both /m/ and /b/ readings these days (and Chinese has all 3 starting with
`/w/`).

So, the reason why kanji are unclear are usually:

  1. Japanese borrowed them badly in the first place because it didn't have the right sounds to say them properly (eg 花{か} ZH: `hua`)
  2. Japanese borrowed them properly, but then its phonology changed and now doesn't resemble as much (eg 絵{え} from ゑ ZH: `hui`, said like "hway")
  3. Chinese was in a transitional phase when Japanese borrowed them, so Japan took a few pronunciations all from the same Chinese dialect (eg 聞, read as ぶん and もん)
  4. Japanese borrowed properly, and just corrupted them (eg 良{りょう} as ら)
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