Set user level permissions to all the privileges for Note except for the read permission. Then they can only create and write for their own notes on that record. They can't do anything with a note that someone else owns.
If you need to lock the user down from modifying his own note, that will be more difficult since inherently users are allowed to modify their own records. You may need some custom code for the OnLoad event that just sets all notes to read only.
Jason Peterson