Even with irregular cycles, ultrasound and LMP both give a rough idea of when conception would have taken place. (especially ultrasound) Either way with both dates, DNA testing has to be done as the dates are far too close to even guess
My periods have never been regular. Different people ovulate at different times. I could go months without a period and that was normal.....
It seems, if your last period began on July 21, that the likeliest date for ovulation is about two weeks later, if your cycles are regular and of average length. This would put conception closer to August 4, but do remember that sperm can live four or five days in your system after sex. If you and your husband split in the beginning of August, you can't speculate on the difference between, say, August 1 and August 4. The dates are so close that if your twins are fraternal, you could even have one baby from one father and one from the other. You really are going to need to do two DNA tests (one for each baby) once the babies come.