importing csv file with ragged right format and " text qualifier
The options I can think of are.

Preprocess the file to remove the double quotes using an 'execute process' task. An easy powershell script that could do this for you would be something like :
powershell -Command {cat \yourpath\stuff.txt | %{if($_ -match '&quot;?(\w+)'){$Matches[1]} }&gt;\yourpath\stuffout.txt} 


Process the file as a single column of variable text. Use an execute script task to process each record and apply a regular expression as the one above (&quot;?(\w+)) or one that better serves your business rules. Redirect each non-compliant record to a file to review later.

The second option is more &quot;correct&quot; as your etl will be prepared to report on non-compliant rows. You can expand on your regular expression to make it more specific.