A proper smoothbore 22r shotgun is very effective for rodent control. Here are some rats shot with my Mossberg 340tr smoothbore 22 shotgun my MILs farm. I have no problem within 20 yards or so killing them with one shot. I have had more fun with that gun. Its also great on carpenter bees. I do not have to worry about damage to the wood in the barn. In the photo of the two rats, I thought that I was shooting at one but when I went to look at the rat I found that I had shot 2 with one shot.
Birdshot out of a rifled barrel WILL be effective on birds at 5'-30'. We had an issue with a certain type of bird for years that wood peck holes in the wood siding of our house. Once I taught my wife how to sneak around the front porch and shoot them off of the side of the house, she routinely dispatched 3-5 a day for a month or so. We had to switch to bird shot after I noticed a leak in the side of the gutter. When I pointed it out to her when it was raining one day, she responded, "Yah, I missed one the other day with the .22 and must have hit the gutter." An old Stevens Crackshot was our bird control weapon. Ironically, after painting the house a light color, the birds in question won't touch the siding now.