DateTime dt = DateTime.ParseExact("20180504", "yyyyMMdd", null);
DateTime dt1 = DateTime.ParseExact("20180430", "yyyyMMdd", null);
DateTime dt2 = DateTime.ParseExact("20180510", "yyyyMMdd", null);
if(dt1 < dt & dt < dt2 )
{
project.SendInfoToLog("Между");
}