During my learning process of Russian language, i use my poor English skills to compare these two languages. Could you please tell me which verb group(imperfective and perfective) in the question title is the verb to listen in English? If both of them too(because translator shows up to listen for both of those verb groups) so what is the difference?
Most likely, when listening to a live person or live TV/radio, you want forms of "слушать": "я сл'ушаю", "ты меня сл'ушаешь?" "сл'ушай!"
Listening to a recording, podcast (but not to live broadcast) - "просл'ушать", "просл'ушивать". "Я просл'ушал з'апись л'екции"
Посл'ушать - the main meaning is past/perfect or imperative of "слушать" : "посл'ушай меня", "послушай эту музыку" (again, if this is about a recording, use "прослушай" instead). "Я послушал это, но не понял". There are other, less frequent meanings of all these forms, for example "прослушивать" means also eavesdropping. "Слушать" also can mean to obey, comply to smb. But I'll stop now. Good luck.