All of my files in home directory have 0620 file permission I don't the the exact reason why, but all the files in my home directory have 0620 file permission. What I remember is that I setup file sharing in System Preference. 



Now, when I try to delete file in my home directory, this dialog box pops up to ask the password. I modified all the files back to permission 0774, but I still can't delete the file without answering the password. 

What went wrong? How can I get the system back to normal?
I use Mac OS X Lion 10.7.2.

ADDED

Refer to this post also
You must set the permissions of the folder the files are in as well.