The best essential oil for getting rid of toothaches is the Clove Oil.
The essential oil Clove Oil contains eugenol, which is used in dental cement and fillings so it's the best and at the top of the list for treating toothaches.
A few other good essential oils for treating toothaches and getting rid of tooth pain is Lavender Oil, Peppermint Oil and Tea Tree Oil.
I use the Clove Oil whenever I have a toothache though because it works best for me.