Damp Drywall: Insects
Drywall wet enough to push your fingers through, will not dry enough to 'recover' its strength. The paper outer layers will have separated and the inner plaster turned to a mushy mess. 

Definitely expose the affected areas. When water gets into walls it can smell for years. As an absolute minimum, you need to remove all the drywall and insulation which was wet. Then you can begin the drying out process. Vaccum up the insects and then seal the dust bag in a zip lock polythene bag for disposal. 

If it still smells funny after a while, some folks like to paint everything on the inside the opening you made in the wall (similar to repairing fire damage) to 'seal' in any odd smells. Just a thought...