English has merged the dative and accusative cases into a single objective case.

Objective-case "her" can thus correspond to German dative ihr or accusative sie.

In this case, it's the direct object of einstellen and so you need the accusative case: sie.

jemanden einstellen is to hire an employee. It's not used for cars or objects.

vermieten is to hire out (i.e. to lend something in exchange for money).

heuern is not a common verb; I'm not sure when I would use it. anheuern might be used for employing a sailor, but it sounds a bit odd outside of a nautical context.

You used the wrong verb -- jemanden entstellen is to disfigure someone. You need einstellen, to hire.