Is money earned from exploiting a portion of a business's goods without the owner's knowledge permissible or forbidden, and does the ruling differ if it is done with his knowledge?

Your disposal of your employer's money without his permission is forbidden (haram), a betrayal of trust, and an invalid act; because you have disposed of someone else's money for your own benefit.

As for the profits resulting from this sale, the more cautious approach is to adopt the view of the Hanbalis and Hanafis, which states that the profit belongs to the owner of the money, and the usurper gets nothing. Meanwhile, the Malikis and Shafi'is hold that the profit belongs to the usurper.