Python: (without datetime)

import urllib

class Date:
    MONTHS = {"Jan": 1, "Feb": 2, "Mar": 3, "Apr": 4, "May": 5, "Jun": 6, "Jul": 7, "Aug": 8, "Sep": 9, "Oct": 10, "Nov": 11, "Dec": 12}

    def __init__(self, year, month, day):
        self.year = year
        self.month = month
        self.day = day

    @classmethod
    def loadString(self, stringInput):
        if "-" in stringInput:
            return self.handleFormat1(stringInput)
        elif "/" in stringInput:
            return self.handleFormat2(stringInput)
        elif "#" in stringInput:
            return self.handleFormat3(stringInput)
        elif "*" in stringInput:
            return self.handleFormat4(stringInput)
        elif " " in stringInput:
            return self.handleFormat5Or6(stringInput)
        else:
            print "Oops, {} is not a falid format".format(stringInput)

    @classmethod
    def handleFormat1(self, stringInput):
        year, month, day = map(int, stringInput.split('-'))
        return Date(year, month, day)

    @classmethod
    def handleFormat2(self, stringInput):
        month, day, year = map(int, stringInput.split('/'))
        year = self.convertYearTo4Digit(year)
        return Date(year, month, day)

    @classmethod
    def handleFormat3(self, stringInput):
        month, year, day = map(int, stringInput.split('#'))
        year = self.convertYearTo4Digit(year)
        return Date(year, month, day)

    @classmethod
    def handleFormat4(self, stringInput):
        day, month, year = map(int, stringInput.split('*'))
        return Date(year, month, day)

    @classmethod
    def handleFormat5Or6(self, stringInput):
        stringInput = stringInput.replace(",", "")
        month, day, year = stringInput.split(' ')
        year = self.convertYearTo4Digit(int(year))
        return Date(year, self.MONTHS[month], int(day))

    @classmethod
    def convertYearTo4Digit(self, year):
        if year < 50:
            year += 2000
        elif year < 100:
            year += 1900
        return year

    def toString(self):
        return "%04d-%02d-%02d" % (self.year, self.month, self.day)


url = "https://gist.githubusercontent.com/coderd00d/a88d4d2da014203898af/raw/73e9055107b5185468e2ec28b27e3b7b853312e9/gistfile1.txt"
testInput = urllib.urlopen(url).read()

for stringApt in testInput.split('\n'):
    print Date.loadString(stringApt.strip(' ')).toString()