I am experiencing the exact same thing on my phone Lumia 620 - for the last couple of days I've burned through 3GB of data which I normally wouldn't even manage to use throughout an entire month and the battery get's drained within few hours. I don't have any auto backup running - the phone is constantly on battery saver. As mentioned by other users Data Sense also claims that the Streaming Media is the big user. My phone is now complaining about 'limited space on the phone' which I would think is also an indicator that it's obviously not online backups being uploaded rather it's something unknown being downloaded.
I have tried using a program called Fiddler2 to track the phones connections via wifi through my laptop
Monitor Windows Phone. Which works and shows any connections you might have. The problem however, is that the huge data consumptions and battery drain only occurs when when the cellular network is 'on' and the wifi is 'off' - the opposite does not cause any huge downloads via wifi.
Now I've consequently turned the wifi 'on' and the cellular 'off' waited for a day then vice versa the next day. When only the 'wifi' is on no alarming data consumptions is going, though when the opposite is the case the data streaming media began downloading again until no more space was left on my phone.
I've uninstalled quite a few apps trying to pinpoint the causing app as well as releasing some much needed space on the phone. The problem however still persists and I have not at any point had any video streaming applications installed like metrotube, youtube ect.
If anybody is familiar with an application or software that can track the usage of the cellular data that would be very helpful. I've called my carrier (a danish company named 'CallMe'), though by law they can't track any information of the actual data being sent and downloaded, so no help there.
Should it be that some cloud downloads might be the cause of it - I have recently updated my windows 8 OS on both my computer and laptop to windows 8.1. I don't know if Skydrive/Onedrive now has some odd syncing going on.