The tone in "Thank You, M'am" is what I would call informally conversational. Hughes is not trying to impress anybody with his vocabulary or complicated writing style—he is just trying to tell his story in a straightforward, simple way, like you might hear it from a friend.
This tone is apparent in some of the phrases he uses. At one point he refers to Roger as “the being-dragged boy” because Mrs. Jones has overpowered him and his hauling him back to her apartment, much against his will. We also hear this informality in Mrs. Jones’ speech, which sounds uneducated but morally upright, as evidenced by her comment on Rogers attempt to steal her money to buy blue suede shoes: “Shoes come by devilish like that will burn your feet.”