Can it be assumed that this is an "average" person? As opposed to say a trained singer with perfect pitch and years of articulation training from singing Gilbert and Sullivan, say. When you say efficient, do you mean in bits/time or efficient in the sense of phonemes per byte?

yes, I am talking about an average person. When I say efficiency I mean the combination of speed and clarity. An efficient method needs to be fast and easily understandable.

Does it have to specifically be voice, or is any analog sound produced by humans acceptable? Is the decoding agent a human or a computer?

Think of it as a conversation between two humans. But instead of words they speak binary data. Any sounds that can be reliably produced and differentiated by the average human are acceptable.

You could yell capital letters and whisper lowercase ones...

What's stopping you from using a system similar to Morse code and just use clicks and pauses for the zeros and ones?

As I said, I want maximum efficiency. Although it is better than spelling out ones and zeros it is still quite slow and would probably be prone to misunderstandings.

Also, welcome to the site, to answer to a specific person's comment, use @(name of the person).

This reminded me of the old modem sounds

As others have pointed out, you can encode "meaning" to any number of variables in speech (volume, pitch, pause, etc.) but your question seems to ignore those and focus on number of syllables as your measure of efficiency. That makes it a LOT more answerable -- was that your intention? Otherwise this quickly devolves into "how many distinct phonemes or levels of [amplitude, frequency, time, etc.] can be discerned?" (and how reliably -- there's a reason why we might prefer "alpha bravo" to "A B" even though it's slower)

Two average people are talking: one is describing and the other is listening. Have they planned for this exchange, e.g. is it part of a professional role that they studied and trained for, or are these two normal, modern-day people who suddenly have a need to communicate binary-data and they need a quick-and-easy method?

And if they're just two people who haven't trained for this in advance, how much data do they need to exchange, and are they under time-pressure? This is, do they have time to talk about how they're going to efficiently communicate a lot of data, or do they just need to come up with a simple encoding system for immediate use?

Relevant xkcd

The military Alpha, Bravo etc is a very well-known 26-character alphabet, so you just consider your image as a many-bits integer which you encode in base26. You might want to add error correction bits.

People always strive for efficiency and would quickly invent some simple, yet way more effective tool. Why would they want to use just voice?

Even the librarian could utter the source code for the image viewer, just saying Ook!.

If speed were the primary consideration and we knew the audio transmission would be clean, a beat-box encoding would probably be both pretty effective and damn fun.

@A C it can be any sounds. Sounds used in the english language are just a subset. As long as the can be reliably reproduced and understood by humans they are acceptable

@Nat yes, they have planned for this. I haven't really nailed down the amount of data that needs to be transmitted, as I want it to be dependent on the method of transportation. There is no time pressure but the participants want to be done eventually.

@Oleg V. Volkov the only way they can communicate is by voice. They have no other choice if they want to transmit binary data.

Words are already pretty information dense.