Open Broadcaster Software has a portable mode that users can install to USB storage devices. The application is free to use and is available for Windows, Mac OS X and various Linux distributions.
After installing Open Broadcaster Software to a USB device, create a shortcut to OBS.exe. Right-click on the shortcut and click Properties. Next, type -portable at the end of the Target line and click OK to save the change. Finally, move the new shortcut into the USB device. Adding -portable causes the program to store the application settings in the USB device, rather than in a local folder.