There's no Finder command to delete a file outright. The function is "Move to Trash" and has the shortcut command+delete.
What exactly are you doing that is prompting this dialog box to show up? Also, can you post a screen shot of it? (Hit command+shift+4 and then hit spacebar to capture a single UI element like a dialog box.)
You may get an authentication dialog if you try to delete system files, but there should be no warning if you just want to move something, say, on your Desktop to the trash. I would recommend that you actually keep the "Show warning before emptying the trash" selected so you can move as many files as you like to the trash freely and then get confirmation when deleting them for good.
The only situation where files will be deleted outright instead of being moved to trash is when you are working on a network share. That is normal behavior.
One last thing: make sure that the trash actually exists by opening up Terminal and running
ls -la ~
One of the first few lines that comes up should look like this:
drwx------ 3 nreilingh staff 102 Feb 6 13:26 .Trash
. makes it a hidden folder, and your user should have write access.
EDIT: I suppose it's possible that the permissions repair you mentioned didn't execute completely or properly. I would do that (and a disk repair) again just for kicks, and then start searching the filesystem for extended attributes. Perhaps the OS has labeled your homedirectory with an extended attribute that prevents it from trashing normally. No idea why that might have occurred, but there are only so many things that can go wrong.
Also to be sure, is you filesystem structured normally with everything in a standard OS X hierarchy on the main boot disk?