Do I need to have copies of the files on my computer that I have on OpenDrive?

It depends on how you are using OpenDrive. It is possible to store your files without having to keep copies of those files on your computer. OpenDrive is designed this way to enable you to save space on your computer by using OpenDrive as you would another hard drive. It also permits you to back up all essential files to OpenDrive in case you need to do a system restore due to a fatal system error and/or virus attack.
However, if you wish to synchronize files on your computer to OpenDrive, you must have the files on your computer for the OpenDrive sync job to compare with.