Read, write, speak and?
Solution 1:
In the context of learning a language, we often speak of being able to read, write, speak and listen to it.
Solution 2:
Isn't "I can understand ....." referring to the fact that one has the ability to understand audio/spoken words/sentences?
We often use, I can read/write/speak to differentiate between the abilities to read/write/speak.
My best bet for ability to understand audio, in common usage is on "I can understand...."
Solution 3:
Write, read, speak and . . . ? The only word that fits is understand. I know that understand can be used of writing as well, but the context will almost always show what is meant.
Solution 4:
The OP notes that one is said to read if one can understand written text.
He adds, somewhat superfluously I think, that one can understand information provided in written or audio form.
The OP then asks for:
a single word that means only the ability to understand audio
I think the answer is no, there is no single word primarily understood to mean that. I'm with Gnawme that hear does have that meaning, certainly more so than listen, which was also suggested, and would fit most elegantly into the role.
However, I don't believe that particular meaning of hear is limited to information received via audio. For instance, one might respond to sentiments expressed in an email with the reply, I hear you.
Primarily, though, the problem I see is that hear is so much more commonly used and understood to mean simply : to perceive or apprehend by the ear. To hear audio would then pair more closely with to see written information, rather then to read it.