With difficulty, because you're looking for negative data.
What you probably need to do is build a list of what groups are used and then subtract it from the list of all groups. You'll need to look through all the project roles, all the permission schemes, all the notification schemes, all the security schemes, any group field data, all the filters and all the gadget definitions to find out where groups are being used. I can't think of an easy way to do any of this in one go.
Again, there is no way to do this because you can not search for a negative value.
You need to
Some extra points here
Again, get the list of groups, then subtract the list of groups in use from it.
You also need to think through what you mean by "groups used".
If you read the permission scheme table, you can extract lines where you've got "allow permission to group X", but that doesn't cover the use of groups via role. Or group-picker custom field.
It should be easy to change Tiago's SQL to something that will get you the groups in the schemes though.
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