Q: This hole appeared under the edge of my screened porch. There was a VERY large amount of dirt displaced from the dig. Any thoughts as to what it might be and how to deal with it? If it is a rat, I am to blame as I am feeding birds nearby.
A: It surely looks like a rat hole to me. Your mention of bird feeding confirms it. If you use bird food that contains lots of cracked corn or wheat or millet, birds will scratch it to the ground where rats, squirrels and chipmunks eat it.
Stop feeding the birds for at least a month. If you want to do it again, use black oil sunflower seed, which song birds are not likely to waste.