How to repair permissions after removing the "wheel" group from my hard drive?
This not-really-an-answer answer probably doesn't solve your problem, though the result is so astounding/interesting not to dump it in the comment section:

I set up a virtual machine with Snow Leopard Server (10.6.8). After deleting (not just disabling rwx!) all wheel group permissions of /bin, /sbin, /private, /System and all subsequent files and folders as well as those of all relevant folders in /Library with either an admin or the root account and afterwards totally removing the group wheel with the workgroup manager, the system still boots properly. Some apps don't work properly (e.g. Terminal in the admin account; it still works in the root account).

Consequently I can't reproduce your problem.

You may try the following in Single User Mode:

At the prompt enter:

/sbin/fsck -fy
/sbin/mount -uw /
launchctl load /System/Library/LaunchDaemons/com.apple.notifyd.plist
launchctl load /System/Library/LaunchDaemons/com.apple.diskmanagementd.plist
launchctl load /System/Library/LaunchDaemons/com.apple.securityd.plist
launchctl load /System/Library/LaunchDaemons/com.apple.configd.plist
launchctl load /System/Library/LaunchDaemons/com.apple.diskarbitrationd.plist
diskutil repairPermissions /


If the loading of com.apple.configd.plist doesn't find an end you may just enter launchctl load /System/Library/LaunchDaemons/com.apple.diskarbitrationd.plist or after entering ctrlC continue with launchctl load /System/Library/LaunchDaemons/com.apple.diskarbitrationd.plist

If you don't get a new prompt :/ root# after waiting some time, you may just enter the next command. You may also modify the sequence of the five load commands. I needed three attempts to get that working.

You should now see a wall of notifications. It should take about 20-30 minutes to repair everything.