gistfile1.txt

public static bool IsOverlapped(string start1, string end1, string start2, string end2)
{
    CultureInfo enUS = new CultureInfo("en-US");
    DateTime dateStart1, dateEnd1, dateStart2, dateEnd2;
    string dateFormat = "yyyymmdd";

    if (!DateTime.TryParseExact(start1, dateFormat, enUS, DateTimeStyles.None, out dateStart1))
        throw new ArgumentException(nameof(start1) + "is wrong format");

    if (!DateTime.TryParseExact(end1, dateFormat, enUS, DateTimeStyles.None, out dateEnd1))
        throw new ArgumentException(nameof(end1) + "is wrong format");

    if (!DateTime.TryParseExact(start2, dateFormat, enUS, DateTimeStyles.None, out dateStart2))
        throw new ArgumentException(nameof(start2) + "is wrong format");

    if (!DateTime.TryParseExact(end2, dateFormat, enUS, DateTimeStyles.None, out dateEnd2))
        throw new ArgumentException(nameof(end2) + "is wrong format");

    return dateStart1 <= dateEnd2 && dateStart2 <= dateEnd1;
}