PCOD, LMP-10May14, IUI-30May14 positive pregnancy test on 19Jun14.my pregnancy is of how many weeks? When shall I expect baby's heartbeat in ultrasound?

You can... Detect a heartbeat sometimes at 5 weeks to 6 weeks.
4 weeks 6 days. If your IUI was May 30 , that is your conception date, and your LMP is not relevant. That makes you 4 weeks and 6 days today. Your due date is Feb 20, 2015. A heartbeat can be seen as early as 5-6 weeks, but the best time to do the ultrasound to make sure everything is ok is 8-10 weeks.