I've had success with a couple of different techniques - depending on the personalities of the dog.
One was VERY food motivated. So every time a storm would start up and she'd start getting anxious I'd get the treat jar out and every clap of thunder or flash of lighting I'd laugh and dance around, gave her treats and just be really happy and make it like a big party. It didn't take too long for her to hear the thunder and run to the kitchen barking and jumping wanting her treats.
Another sounds much like your Odie. She'd shake and hyperventilate to the point of nearly having a seizure. Wasn't just thunder and lightening, it was any loud noise that she couldn't see the cause of the noise. The A/C kicking on, the garage door going up, heavy rain. With her I just had to stay very calm, she could sense if I was upset, and kept her laying right on my lap. Very little petting, no comforting talk, just an occasional scratch on her back and when it started to get out of control a firm but loving "Quit". If it was at night, I'd turn on a night light and at first even the tv to help with the noise issue. It took maybe a year, but she got to where she'd be worried, but not freaking out.
The comforting talk and petting that we instinctive want to do only reinforces the fear. They are panicking and you are basically telling them they are right to panic, there is great danger and you should be very afraid. I think it took longer to 'train' my husband to not comfort her then it took her to figure out the world wasn't coming to an end.
I guess the main thing is to find what you can do to get their mind on something else and then do it without transmitting the stress
you are feeling about them being upset.
Good luck!
Teresa