He sat and listened to the radio.
I read the English as “He was sitting and listening” (Estaba sentado escuchando la radio), but the translator makes another, state-changing interpretation.
I’m curious: How do native speakers of English read the English sentence?
As a native English speaker, one of the hardest differentiations to make is between the preterite (e.g. hablé) and the imperfect (e.g. hablaba) since they are often translated the exact same way into English (e.g. spoke). Without the form “was (verb)+ing”, I usually default to the preterite (sometimes incorrectly, still).
So in your example I would go with se sentó y escuchó.
In other words, he grabbed a chair and started listening to the radio? Sorry if I’m being dense, but this has been bugging me for quite some time.
No problem! I see what you mean now and have never thought about this before.
Without any context, I read it actively like “he (grabbed a chair and) sat (himself down) and listened to the radio”.
But I would read it the other way if there was context, like: “Ït rained all day. He sat and listened to the radio.”
As a rule, I use the imperfect whenever I could use “would always”, “used to”, or “was -ing” without changing the meaning of the sentence.
For all other past situations, I use the preterit.
OK, thank! I’ll have to recalibrate my brain a little 
I seem to have forgotten about the past continuous, which would obviously be used if he was sitting listening to the radio.