"I am listening to them."

Translation: Słucham ich.

[roxyphuong]

Why can't I say "Słucham je"?

[Jellei]

Wrong case. Słuchać mostly takes Genitive*, and Genitive both from "oni" and "one" is "ich". But if you were to say, for example, "I like them", that would take Accusative and be "Lubię je" (or "Lubię ich" for masculine personal). Also note that if you were to use any preposition before any of them, then they would change into 'nich' or 'nie', respectively.

*Apart from the situations when you're directly addressing someone: "I'm listening to you", then it takes Accusative. But obviously that's not the situation in this sentence.

[roxyphuong]

Thank you so much for the explanation!

[FabienVign1]

What about ich słucham?

[Jellei]

You shouldn't start a sentence with a pronoun any other than the subject pronoun.

[JoeMartino12]

Słucham do ich? That doesn't work?

[Jellei]

Nope. In Polish you "listen someone/something".

Plus it would be "do nich", some pronouns have special forms used with prepositions.