It won't help to keep the kind of bugs that matter to birds, such as lice and mites, which live on the bird. It *might* mildly help with external bugs, such as roost mites, but to a very small degree, if any.
The only oil I know of that helps with mites is orange oil. It has been shown to be effective with ants, spiders, and mite type bugs. However, after using it for a bit (in the coop, not on the bird), I noticed it lost efficacy, and I was back to permethrin.
Birds can also be sensitive to oils, so I would be sure to have good ventilation in the coop if you desire to place herbals with oils (such as the peppermint).
Never use thyme (oil). That has shown to cause death in chickens when placed in their coops.
Research is being done on oregano oil for internal remedies (worms). Unfortunately essential oils are not controlled such that you can be assured of getting the same potency from one bottle to the next. However, that area is promising. A number of organic hatcheries are using oregano oil in the water to help with internal parasites.
Most whole herbs simply aren't potent enough to do the job.
There is this thread which has discussions about herbals and such:
https://www.backyardchickens.com/th...ad-ots-welcome.729605/page-3899#post-18056723
Try posting there to see if anyone has good experience (ie actual improvement of a known condition rather than assumption that it is doing the job because they haven't seen any).
I'm always hopeful for herbals, as I like the idea, but sadly, they have not lived up to the hype thus far for me.
LofMc