_Despite the question seems to have reached its own solution, I'd like to make a new answer, for I find the existing explanations do not lead to correct understanding of the topic._

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All these words have their own meanings usually not directly translated to English affixes like "non-", "in-", "un-", "-less" etc., so I'm going to explain them descriptively. What they have in common is negative meaning and ability to attach to 漢語 ([Sino-Japanese][1]) words.  
(I didn't consider much about two-character compounds like 不安, 非道, 無常, 未婚 etc. because these words are better memorized en bloc.)

### In principle

 - `不～` (read ふ)  

   1. makes **state** from **action**, the outcome is usually a **noun**  
   "not to _action_", or "no _action_-ing"
   > 不使用, 不変化, 不合格

     In this usage it's *tenseless* negation, that is, `保存料不使用` "No preservative used" doesn't only mean "unused" but "never be used". Some speakers may also treat this as a formal way of saying `～しない（こと）`.

   2. makes **state** from **state**, the outcome is usually an **adjective noun** (形容動詞)  
   "not being _state_", "being low on _state_"
   > 不誠実, 不人気, 不健康

     Almost limited to subjectively undesirable state.

 Can also attach to native words.
 > 不まじめ, 不[行]{ゆ}き届{とど}き, 不ぞろい

 - `非～` (read ひ)  
 makes **identity** or its **holder** from **state**, the outcome is usually a **noun**  
 "not belonging to _state_" or "being other than _state_" or "non-_state_"
 > 非公開, 非会員, 非現実

 Maybe better explained as logical NOT. If only two options are in question, it's equal to "un-".

 Can attach to any kind of words.
 > 非ユークリッド, 非割り込み

 - `無～` (read む)  
 makes **state** from **thing** or **action**, the outcome is usually a **noun**  
 "without _something_" or "_something_-less"
 > 無重力, 無公害, 無所属

 Can attach to any kind of words by theory, but other means are preferred outside 漢語: `底{そこ}無{な}し`, `バリアフリー`

 - `未～` (read み)  
 makes **state** from **action**, the outcome is usually a **noun**  
 "not yet _action_-en"
 > 未確認, 未成熟, 未解決

 This one is preferred when the action is considered [telic][2] (i.e. has a goal), even if you do *not* really have intention to achieve it.

**Extra**

 - `不/無～` (read ぶ)  
 makes **state** from **anything**, the outcome is usually an **adjective noun**  
 "ill-_something_" or "mis-_something_"
 > 不器用, 不細工, 無愛想

 Though of high frequency it may be seen in, it's no more productive (i.e. able to make new words using it), and technically it's less related to those ones above, for attaching only to those almost-nativized 漢語 words.

### Actual usage

However, existing words with these prefixes often betray your expectation on how it works, mainly because:

 - Bare 漢語 words are by nature flexible in grammatical status, as like in original Chinese, as well as some English words (round (n), round (v), round (adj), ...). You should fill in implicit participlization. That's why I avoid to use "verb" or "noun" etc. in the list above.  
 e.g. `非表示` → "being-other-than display**ed**" = "undisplayed(ness)"

 - In general, established nouns that mean qualities easily turn into adjective(-noun)s in Japanese. Many common words which should be "noun" according to my list, are actually adjective nouns.

 - Modern Japanese (Meiji–WWII) embraced many words in different word classes than today's. Besides, words themselves could have undergone changes regardless to its original meaning.  
 e.g. `不経済` → "diseconomy" or "being-not econom**ical**" < `經濟` _ModJ_ "economize"  
 `非常識` → "non-common-sense" → "lacking in common sense"

Samuel Martin's _A Reference Grammar of Japanese_ has [a good summary and discussion][3] on those prefixes, but note that he has erroneous analysis on some words regarding the said matters.

**Acknowledgement**: Thanks to @snailboat for references and advice.


  [1]: https://en.wikipedia.org/wiki/Sino-Japanese_vocabulary
  [2]: https://en.wikipedia.org/wiki/Telicity
  [3]: http://books.google.com/books?id=SszxbMtHbs8C&pg=PA388#v=onepage&q&f=false