I don't know how you learned grammar, but that particular point you're having trouble with may be easier to understand through the functions of Japanese particles rather than the meaning of the verb 聞こえる.
In English, word order typically dictates which noun refers to who did the action and what gets the action done on. For example, the only difference between "X hears Y" and "Y hears X" is the order of words. In the former, X specifies "who does," and Y is what is heard. In the latter example, the relation is the opposite: Y is the one who hears something that is called X.
In Japanese, word order doesn't generally function this way. Instead, particles such as は, を, and に do this job. In your case, the problem is that you're implicitly assuming that particle が must take a unique, predetermined function (or meaning if you will) when preceding the verb 聞こえる. This assumption is not correct, and technically it may take any of the various functions/meanings が has.
As you probably already know, が may work to specify who/what does the action described by the main verb, e.g., 友達が家に遊びに来た (My friends came to my place). It can specify what is the target of the verb, e.g., これが好き (I like this). There are many functions when it comes to particle が, and it's impossible to explain them through English translation and English grammar in a simple manner. But the point you're trying to understand may be understood this way:
The が in 変な音が聞きこえる is specifying the target as in これが好き (I like this) while the other が in 皆が聞きこえるようにはっきりと話しなさい is working as a marker for "who does it."
All three examples in OP are grammatically correct and have natural interpretations. The first translation for each sentence is the most likely one.
If you show "Xが聞こえる" without giving any further information about X, the most natural interpretation of the sentence is "I hear X." Pretty much every native Japanese speaker interpret it this way. In this sense, what you learned isn't completely wrong. However, depending on the actual content X and context, が may work as a different kind of grammatical marker. The example sentence 皆が聞きこえるようにはっきりと話しなさい is a good one for this.
If you want to avoid ambiguity, you can use に for this particular case: 皆に聞きこえるようにはっきりと話しなさい. The functions of が and に are slightly different here, but the end results are pretty much the same. If this example is taken from native material, probably the concept the speaker had in mind matched the が version better, though they're the same difference, if you ask me.
If you're perplexed by the fact that が can have two functions in Japanese, think of how English word "if" works. You say, "Please let me know if you need help." What do you really mean by this sentence? There are at least two possible interpretations:
1. You want the listener to tell you whether he needs help.
2. You want the listener to tell you should he end up in a situation where he needs help.
The former interpretation is possible because "if" can mean pretty much the same thing as "whether" in this kind of sentence. But "If" also means "provided that," "on the condition that" or something along those lines.
Your question has nothing to do with は, and every Japanese example given in your post sounds natural and correct. Aaand you won't come back to this thread again, I don't think... Oh, well. I'll post this anyway.
