Learn English – a “high-level conversation”

There are two parts to this expression:

1) to keep an ear out - This is a figure of speech that means to actively gather information on a particular subject. In the context of this story, the subject concerned (I think) is their escape from somewhere? Correct me if I am wrong as I only quickly browsed through the story on the Net.

2) on the street - Again this is a figure of speech. This does not mean physically on the street but just in public in general.

You are right to say it isn't an antonym of big words. The meaning used here is number 11 at the reference:

11. characterized by or indicative of littleness of mind or character; mean-spirited; petty: a small, miserly man.

with a possible additional implication of the twelfth meaning:

12. of little strength or force: a small effort.