It's not the imaging machine itself, but the dyes used (iodine for CTs and gadolinium for MRIs) that can cause the immediate problems.
The machines themselves aren't great either though. They're worse than the dye. All that radiation causes a lot of damage at the cellular and molecular levels. You usually won't feel the problems until down the line when you have cancers and leukemias showing up. They say the radiation exposure from 1 CT scan is around the same as 250-500+ x-rays.
They don't know the long term effects of MRIs yet, but I've seen stories of people feeling bizarre for a while after getting one. MRIs expose you to a magnetic field 25,000-50,000 times the strength of the Earth's magnetic field. I'm quite sure that can't be too good for you.
It would have been nice to have found natural health and this information last year before I received 3 head, 1 neck, and a full length spine CT scans, along with 20+ x-rays of my head, neck, and chest - all done in around a 6 month period!
Fortunately there are ways to combat the radiation poisoning. Like miso soup, seaweed, fasting, etc.