Strain Gauge on LEGO Bridge
Lego bricks can withstand a fairly high pressure before they deform, but Lego creations tend to deform more easily at the various connection points. Therefore it's possible to build a relatively easily deformed bridge using long pieces, such as technic beams. You could build a bridge that deforms easily and then show how it flexes under the various weights.

As for using a real strain gauge, that might be overkill, but if your bridge is fairly bendy you could probably compensate for whatever structural rigidity you'll get from the guage itself. Also I'd go with putting the gauge on a separate, flexible piece (such as paper or plastic) and just pin it to the bridge using normal lego parts. Presumably you don't need super-accurate measurements for this demo?

Lego also has some springs and shock absorbers which can possibly be used to help with your design. Either use them to make the bridge flexible, or use the compression of the shock absorber as your measurement of how deformed the bridge is.