Are you sorting your records by choosing sort from the records menu or by running a script?
Just selecting Sort from the records menu should not create new blank records, but if you are sorting in the default ascending order, any blank records will automatically sort to the top.
Since you are unable to delete these records, it's very possible that your file is damaged or that a field's index is corrupted.
Try recovering the file and test the recovered file (even if no problems are reported) to see if the recovered file works.
Best practice is to not use recovered files, but to import the data from them into a clone of an undamaged back up file if that is at all possible.
You can also rebuild all your file's indexes by importing all the data into an empty copy (clone) of your file.
If you have FileMaker 11, you can also use Advanced Recovery options to rebuild your file's indexes:
With the file closed, select Recover from the File Menu.
- Select "Use advanced Options"
- Select only: "Copy File Blocks as-is" and "Rebuild Field Indexes Now".