Poison is the most effective. FWIW, there are different poisons, some of which are metabolized into harmless compounds by the time the rodent dies. Other poisons kill the rodent but the amount the rodent ingested was small - won’t kill a larger animal. So, do your research into the options you have. And, absolutely, use the bait stations do any poison dies not get removed by the rodent, and nothing else can access the poison.
Just today, I was at a farm store I do not normally go to. They had an aisle for poisons and an informative sheet on the various poisons by a particular company…it detailed the active ingredients and how quickly it would kill, and how they worked.
rodents usually go back to their nests to die, it is not common for them to end up where a chicken would find them. But, in many cases, when a BYCer resorts to poison bc nothing else controlled the population, they keep animals inside, and put poison out only at night when other animals inside. In the morning they scan for any poisoned or dead rodents to remove them before animals come out.
Irregardless of traps or poison or any other method, if there is food in the run, leftover tidbits for the rodents, they will be hard to eradicate. In order for any method to work, the rodents need to want to eat or investigate your poison or trap, so make sure everything is clean and feed free. Buy metal trash cans or rodent proof storage for all your feed, sweep up spilled feed, use feeders that minimize feed loss, don’t throw down scratch- put it into something with sides.