If you have an EVA9150 (i.e. an EVA that supports a hard drive), then the answer is yes you can. You need to go into the EVA Supervisor menus under Advanced settings -> Power and Hard drive, and then enable File Sharing. Once you do this the EVA should show up under your Windows Network Neighborhood and you can drag-and-drop files over to it.

Also on the question of playing stuff from the EVA hard drive I'm assuming the question is "can I stream stuff from the EVA hard drive across the network?". The answer is technically yes, but the EVA really isn't designed to be a file server so the access speed is not very fast. (In other words, I wouldn't recommend it.) If you want to do something like this, I would recommend you get a NAS storage box and put it on your network. (Such as the ReadyNAS Duo) Then any files you put on the NAS box would be accessible from any of your network devices, including the EVA.