Google last year released a file management app called Files Go for Android devices. It comes with an AirDrop-like wireless file sharing functionality as it takes advantage of 5GHz Wi-Fi Direct capability in supported devices to support the highest transfer speeds possible.
Google recently updated the app with support for USB OTG. You can now access external USB storage device and move files. You also have the ability to view full folder structure on the phone or any connected device.
Download the updated app from Google Play Store.