You may be able to tell by looking closely at any existing penetrations of outer walls such as plumbing or electrical openings. If none of these exist, try removing a switchplate on an outer wall and inserting a wooden or plastic, not metal, probe. Definitely turn off the power first.
If this doesn't work, you may have to drill or cut a small hole in an outer wall from a hidden location like a closet or a utility room. You can also try looking in the attic.
An energy audit will reveal insulation levels in all areas of your home. An auditor uses specialized equipment, such as an infrared camera, and knowledge of construction practices and materials peculiar to your home's age and location to determine if walls are insulated.
You can also get a rough estimate of the insulation levels in walls by using an infrared thermometer that can be purchased at automotive or larger hardware stores for around $50. By comparing the temperature of interior versus exterior walls, a homeowner can get an estimate of the amount of insulation in walls. The North Dakota Extension Service outlined the process in the publication linked below.
Determining Insulation Levels Using an Infrared Thermometer
