The most important of the basics of deterring/discouraging rats is to take away their food and shelter. So, things like putting away the chicken's feed at night, sweeping up spilled feed, using spill-resistant feeders, storing feed in rodent proof containers, gathering eggs often. So, things like clearing brush, tall grass, and piles of things away from near the coop because they don't like to cross long stretches of open space. And hardware cloth or metal lath apron out 2-3 feet or down to keep them from digging tunnels under the cement of your floor. Since they are already chewing through the walls, I'd put metal lathe up the walls too. Hardware cloth might work for that too but metal lath is sharp as well as sturdier and was less expensive so I don't think they will be very eager to climb it. I saw the cost of the lath went up lately but haven't looked at the cost of hardware cloth lately.
If they get to the food regularly, and continue to have the shelter of the brush to get in and out - they will start building nesting tunnels under your shed foundation. Take away one of the two and they might not. Take away both and they are most likely to not move in although if they have good habitat not too far away then they will probably check periodically.