I don't think you can; the Task List file is 'per user'.
In XP, you could run Eraser from the Administrator account, but I suspect that this would be no different to running from a user account with Administrator status. Likewise, in Vista and Windows 7, running elevated gives you all the powers a user - any user - can have.
If you want a System Task to get rid of (or erase cluster tips on) those pesky files that Windows insists on protecting, then, regrettably, the answer is that you can't. Short of formatting the drive and wiping free space, that is. That would apply to any Windows application, not just Eraser. If you want to go to the trouble of booting a non Windows OS from an optical disk, and deleting the files from there, you might succeed, but there are some files that Windows will re-create when it boots.
David