Can I keep an older refrigerator, which is empty, running on the warmest setting for an extended period without worrying about smells? Will it save considerable energy by turning it to the warmest setting?
A clean refrigerator will not smell. The air inside would be entrapped and accumulate no other odors. If not fully clean, anything inside that might decompose would not do so at a suitably low temperature. Clean is still better than cool and old, however.
There is no harm in powering off the refrigerator. One can place a magnet on the door frame to prevent complete closing, which would allow any minor odors to escape. I have a dorm sized refrigerator configured in this manner and it does not smell. The door is about 12 mm open (1/2") and when started after three years of being unplugged, cooled properly and ran normally.
You will save energy at the warmest setting but not what I would call considerable. With the door closed and not opened for extended periods, the compressor should not operate as frequently as when in use, but will operate to bring the temperature back to the dial setting as needed. Temperatures outside the refrigerator and the insulation quality comes into play for that determination.
Not a duplicate, but another post to contribute to your question: Unplugging vs running an empty refrigerator
Block the door open
Several times I have seen people shut off fridges not in use. To their surprise, an explosion of mold follows in the fridge. The reason is, refrigerators contain water you don't know about. This humid, sealed compartment then becomes a breeding ground.
I leave the door blocked partially open (like at least 2 inches) for at least a month. I would not then close it unless I had some dessicant packs to throw in there. Dessicant packs, not foodstuffs often misused as dessicant like rice.
It is very important that your blocking scheme is not defeated by some well meaning helper. Some people cannot abide the sight of a refrigerator door open. They will want to close the door, and will think you foolish for wanting to block it open. You will need to deal with those people somehow.
Another option is to remove the doors entirely, they are designed to be easy to remove.