Is it ethical to for a commercial organisation to get student interns to download journal articles using student's university access?
It is unlikely that your use of this journal subscription would fall within the terms-of-usage agreed by the university with the journal providers, and agreed by you (as a student) with the university.  You should enquire further into the particular terms of access for these resources, but I would imagine that they would be restricted to use for educational and research purposes within the scope of your position as a student at the university.

Either of these practices could potentially get you into trouble, though the use of software beyond the terms of the licence is probably more fraught with danger.  Downloading journal articles for work purposes is not that uncommon in fields employing academics and students, though it is probably not legal.  While some forbearance might be given for small infractions, certainly it is unethical to agree to access a resource from the university for the purposes of your education, and then to use that resource systematically to advantage a commercial business that is unwilling to pay for the service.