String to Date parsing

DateTime.ParseExact or DateTime.TryParseExact are appropriate here - both will accept multiple format strings, which is what you need in this case. Make sure you specify the invariant culture so that no culture-specific settings (such as the default calendar) affect the result:

string[] formats = { "yyyy-MM-dd", "yyyy/MM/dd" };
DateTime date;
if (DateTime.TryParseExact(input, formats,
                           CultureInfo.InvariantCulture,
                           DateTimeStyles.None, out date))
{
    // Add date to the DataTable
}
else
{
    // Handle parse failure. If this really shouldn't happen,
    // use DateTime.ParseExact instead
}

If the input is from a user (and is therefore "expected" to be potentially broken, without that indicating an error anywhere in the the system), you should use TryParseExact. If a failure to parse indicates a significant problem which should simply abort the current operation, use ParseExact instead (it throws an exception on failure).