javascript accepting multiple date format
You can use Javascript to give the user the feedback that the correct format(s) is being used. But if you are taking any data to your server be sure verify the data on the server. 
To verify the correct dataformat you can use Regular expressions and check if any format is correct. You should iterate through all allowed possibilities until one is found correct.
I should preface this post by saying that I am a very elementary developer with a generic IS degree. Without going into too much detail, I was given a moderately large web application from an interning software engineer to support an enhance if need be. It was written primarily in Python, JavaScript and HTML5 and utilizes a Google Map API to visually represent the location and uses of given inputs. This leads me to my question.
There is a date picker modal that the application/user utilizes. They pick a START and END date, in the default format YYYY-MM-DD (if the user does not use that exact format (i.e. 2015-09-29) the date picker will not work), and the application then goes to the DB and picks the given inputs between those dates and represents them on the map. I have been told that, for usability, I have to make the program accept multiple date formats (i.e. September 29 2015, 09-29-2015, 9-29-2015, 9/29/2015). How would I go about doing this?