How can I run Linux commands on an Android device?

You can run Linux commands on Android. But there are usually just very few pre-installed. If you want to add more commands you might want to root your device and install busybox on it.

This is not for productive use within an application but can help you to work with your device.

As far as i know, the only way to run shell commands is:

Process proc = Runtime.getRuntime().exec("your command");