Understanding underscore "_" in group permissions & external drives

What's the format of this volume? Is it HFS or FAT? If it's HFS, then it seems that permissions are being ignored even though the info dialog says otherwise. Try checking the box to ignore permissions, then unchecking it. That will cause an update to the volume info database and maybe fix the problem.

The underscore is the group associated with that username. In OS X for each user there is a corresponding group, and that group's short name is the same as the username, except that it has the underscore in front of it. For instance, on my system my username is "tkessler" and there is a hidden group for my account called "tkessler". I'm not sure why the system sometimes puts an underscore in front of the name, but it happens. The underscore name should still reference the same group as the non-underscore version of it (ie, the "_guest" name for the guest group is synonimous with the name "guest").

To make the drive so only you have write access, you can remove all entries except the first one and "Everyone", set your name to be the first one with read and write access, and then set everyone to "read only" and then use the gear menu at the bottom of the info window to propagate the permissions to the enclosed files and folders on the drive.

The wheel group is the default group for people with access to using the "sudo" or "su" commands. Currently your user and group permissions are set so you have full access and the group has no access, so other admins will be denied unless they invoke admin privileges to alter the directory's permissions or view it as root.

Currently, however, you also have the "Everyone" group set for read only, which will allow other users to read the folder's contents. If you do not want this then set it so they will not have read or write access.

If you use the chmod setting as you described, then it will set the folder so everyone can read from it, but only you will be able to write to it.

Do you have more than one admin account on the system? If not then there is no need to worry about the wheel group priveleges.