I had rats last winter that tunneled from one coop run to another. I tried several things and finally landed on an electronic trap that zapped the rats when they entered it.
I didn't have to touch the dead ones, which was much nicer than the giant snap type kill traps. I had also tried those, with limited success.
My attempts at catching mink with humane traps failed, so I skipped that step with the rats.
As far as using strong essential oils to repel the rats, (stuffing soaked rags into their tunnels) I would have been better off dripping peppermint oil into my bath water to help me relax after seeing the vermin.
Since then, I have installed hardware cloth under those two coop areas. I used to feed the ducks in their run, but since they are free during the day, I now have their feed dish about 20 feet away from their home. Also, I have always kept the feed in metal garbage cans.
Good luck in your battle!