Your OneDrive account, and the folders and files contained within it, can be accessed on phones and tablets. Download the OneDrive app from the App Store, and use your MCC credentials to login. Depending on how many files you have stored in OneDrive, it may take some time to fully synchronize. It's best to connect to Wifi when the app is doing the initial sync.
The mobile app should be set to show you the list of folders and files, but only download the file when you click on it. Set like this, your OneDrive contents do not fill up the storage on your mobile device. You can, however, choose to keep a copy of the file on your mobile device. Look for the option "Make Available Offline" to download the file.