Don't HALT a script if you don't need to. Also, don't use HALT unless you're trying to halt everything that happens... use RETURN instead.

Also, you forgot the filename in the delete section and $readn works fine to avoid another search of the file.

Code:
on *:TEXT:!addnewquote *:#:{
  if ($read(quotes.txt,w,$2-)) {
    msg $chan This quote already exists!
  }
  else {
    write quotes.txt $2-
    msg $chan The Quote has been successfully added.
  }
}

on *:TEXT:!delquote *:#:{
  if (!$read(quotes.txt,w,$2-)) {
    msg $chan This quote doesn't exist!
  }
  else {
    write -dl $readn quotes.txt
    msg $chan The Quote has been successfully deleted.
  }
} 


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