Is it permissible to take money for delivering items that are not part of one's core job, even if it's possible to hire someone to do it?

It is not permissible to take money from an employer without his permission. The fact that the tasks are not part of the job duties does not make it permissible to take a wage for them without the employer's permission. The matter must be explained to him, and if he agrees to give a specific wage, then there is no harm.