How to ignore opening quote in views sort
views_natural_sort is able to do this kind of sorting.  

It might be currently in alpha state but it already has more than 250 installation for the alpha 3 release which means that  most major bugs should have already been ironed out.

Upon enabling you are able to choose title to sort with and you are given 2 extra options for natural sorting (sort natually ascending and sort natually descending)



It also has some handy settings at admin/structure/views/settings/views_natural_sort which you will allow you to chose what other characters you want to ignore (and other settings)

Following are the default settings