Energy savings may be gained by building exterior walls thicker to accept more insulation. Thicker walls may save money in some areas where it stays very cold, but other areas may benefit more by adding more insulation in the attic. Whether or not you can actually save money by increasing your exterior wall size, can be computed.
Do you need to winterize your home? Are you leaving for several days or several months? If you want your house to be in perfect shape upon your return, you better do certain things before you walk out the door.
I see miracle energy savings scams all of the time. Some of the things they promise are too good to be true in my opinion. Save energy by doing a lot of small things around your home - use a programmable thermostat, energy saving light bulbs, and more.