I have a basement but there was a tornado very close to my house when Lila was elderly and wouldn’t go downstairs. She did not tolerate being picked up and even if she did, carrying her down the stairs would likely have resulted in disaster. I didn’t know what to do and I don’t know what the right thing to do is. But I decided it would be no good if the house was hit and we were both trapped or injured upstairs so I took shelter in the basement. Lila laid down on her bed in my bedroom. I was terrified. Luckily the tornado passed us over.
If I didn’t have a basement or interior hall, I’d go to the bathroom, probably in the tub with the curtain closed. I don’t think I wouldn’t crate a greyhound out of fear of her being trapped in there. I would definitely have her on a leash. I would crate smaller animals whose crate I could carry.
Tornadoes are especially scary since there is usually little to no warning they are coming so it's good to have a plan.