"Take a look at" is widely acceptable, while "take a listen to" is still trying to earn respect. It still sounds strange to me, but it is as grammatically correct as the earlier expression and should be equally accepted, in my opinion.
I just read the response to this question. Unfortunately, the instances provided hardly justify the propriety of "take a listen." Although this expression is has become increasingly popular by broadcasters, it would help to distinguish acceptability from grammaticality.
In "take a look", "take a walk", etc. "look" and "walk" are nouns; "listen" is not a noun, so "take a listen" - modeled on those other expressions - can be accepted only as a stretch..