If you have a date in a cell, say cell A1, what is the result of this formula ?
=istext(a1)
If the result is TRUE, then it's a text string, which Excel won't automatically read as a date, but there are ways round it.
If the result is FALSE, then it's a number, which Excel probably can read as a date.
For the examples given, can I just check . . .
Is it
6/30/2016
or perhaps
06/30/2016
or perhaps
_6/30/2016 (where the first 6 is preceded by a space character).
What I'm getting at, is, is the length of these text strings ALWAYS 10 characters (2 for day, 2 for month, 4 for year, and 2 / )
OR, does the length vary depending on the number of digits in the day and month ?
Whatever the answer is, we can work round it, but it's easier if we know this in advance.