QUM, Iran, April 26 — A black-turbaned Iraqi cleric, his belongings packed in a small blue bag sitting at his feet, led about 50 clerics in prayer. Kneeling on red Persian rugs, the men, many of whom who had spent the last two decades in Iran, gathered to catch the train that would take them to Iraq. "I am going first to Kazemein for a pilgrimage and then will go to Baghdad to find a home for my family," said Muhammad Hassani, a 52-year-old mid-ranking cleric, who had lived in Iran since 1980. Mr. Hassani, the father of 10, had...