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.
When running as an administrator from a non-admin account on Windows 7 Pro, I get the message "Eraser has stopped working". Sometimes this happens when the status bar shows about half done, sometimes it completes and then upon viewing the task log it crashes. The details are below. When I run under the non-admin account, it simply hangs with no errors showing in the task log. Thoughts/suggestions?
You don't say, but I infer, that you are running a free space erase, very probably on the System drive. If so, this is a known (and complex) issue on which Joel is actively working. Some aspects of the problem have been fixed in the development builds, but we are working to find a way of reproducing the residual problems consistently. Much of the problem is about ways of getting Windows safety and security features not to trigger the crash.
If you are erasing free space on a system drive, try disabling the option to erase cluster tips (which is probably not a major issue for most users). If that doesn't work, uninstall Eraser 6.0.7, and download and install a development build (2221 when I last looked).
If you need to come back, please start a new thread. This one is really on a different issue.