Your question can't be answered.
The anti bacterial and anti parasitic properties of oregano are quite limited. Their active compounds not present in significant quantity, and to the extent they are present, they are concentrated differently in stem and leaves AND vary with the season, the climate, and the soil conditions. Not knowing when your dried oregano was harvested, under what conditions, and how much of those compounds have been destroyed by drying, storage, oxidization, and sitting on the shelf exposed to light.... the concentrations are even more uncertain. Meaning the quantity needed for any reliable effect is uncertain.
But if you look at the studies, the few of any scientific vigor, the concentrated oils they are using wqere obtained from simply stupid amounts of oregano - far more than you are going to get in a spice islands or mccormick jar, and far to pricy to be a reasonable long term solution.
If you want to go the natural route - plant some oregano. Once established, its hard to kill. Your chickens will (largely) ignore it, and it makes a decent ground cover - but you can feel better about yourself for providing it, and it is (seasonally) attractive. Probably more nutritionally valuable for the bugs that like it than its mostly mythical antibiotic properties.
