Not with vegetable oil but Neem oil may make them think twice about laying eggs.

Floating Row Covers can be used to keep the adult Wasps, Moths, Sawflies, Flies, etc. that lay the eggs that hatch into the larva that tunnels into the leaves. Some Neem Oil products might act as deterents or possibly kill the larva as they hatch and before they enter the leaf. Traps, meant to attract the adults, can also work.
Except for plants that you eat the leaves most damage done by Leaf Miners can be cosmetic with no real reason to remove the leaves from the plant.
Many people think that because Neem Oil Products are "natural" they are safe, but like any other pesticide due care in use is needed since these peoducts are broad spectrum and can kill off beneficial insects as well as any pests. I have even noted some refer to Neem Oil products as non toxic, and yet they kill insects so they are not non toxic to those insects.