Moving a used refrigerator

Alas, the refrigerator is dead.

That smoke was the refrigerant escaping. Theoretically, you can patch the hole or holes and recharge it. But that will cost more to get right than buying a new one.

Next time you need to defrost, turn it off and let the ice melt. This will take an hour or two at no risk to the refrigerator. If you need to do it in minutes instead of hours, use a hair dryer.

I think unplugging the refrigerators will both save electricity and reduce wear on the compressors, although I agree with others that if possible you should measure the usage, in part to decide whether any (possibly small) savings is worth the effort.

Energy Savings

Empty refrigerators are less efficient, since the compressor needs to cycle on and off more frequently due to relatively low thermal mass. If you unplugged the fridge when you weren't using it, I suspect when you plugged it back in it would only take a few hours to cool down. Under normal usage a fridge will have its compressor running about 1/3 of the time, so this will be a meaningful savings. (The fridge uses the vast majority of its electricity running the compressor, so how long it's running for is a good proxy for electricity consumption.)

Wear on Refrigerator

Cycling of the fridge compressor on and off is a primary cause of wear, so unplugging the fridge should be a benefit in that respect. Plus there will be total fewer runtime hours. I don't see how unplugging the fridge for days at a time could possibly damage it. (If you were unplugging it twice a day and forcing it to warm up to room temperature and the cool down, that would be another story.)

Other Considerations

• When the fridges are off you will need to make sure they don't get moldy or develop smells. The easiest thing would be to leave the doors open so any moisture can evaporate. Leaving a dry hand towel over the door can help ensure the door doesn't close accidentally.
• If you have the means to measure the electricity savings, I would do so. You may find that the savings are small and not worth the effort.
• Water jugs will not help you if you are unplugging the fridge, in fact they will make it worse. The purpose of the water is to retain cold and stabilize the temperature. If you let the water warm up to room temperature with the rest of the fridge you will just be creating more work for the compressor when you plug it back in. On the other hand, if you decide to keep the keep the fridge plugged in all the time, leaving jugs might help a bit (but only if you leave them in all the time... do not remove them).
• Do you really need two fridges at all? Maybe a cooler and some cold packs could supplement any overflow those 2 days/week?
• Old fridges can be big power hogs. I'm sure you could save a lot of electricity with a new model (maybe a single bigger one). Whether a new fridge could pay for itself in a reasonable amount of time depends on a number of factors, but it might be something to consider.