Is there a simple way to reinstall all packages that my app depends on (i.e. they are in my apps node_modules folder)?
The easiest way that I can see is delete node_modules folder and execute npm install.
Right way is to execute npm update. It's a really powerful command, it updates the missing packages and also checks if a newer version of package alreaddy installed can be used.
Read Into to NPM to understand what you can do with npm.