MELBOURNE—Australia’s east coast was smashed by heavy rains on Saturday, sparking dangerous flash flooding that forced the evacuation of multiple regions as the fast-moving waters unmoored houses, engulfed roads, stranded towns, and cut power lines. In Sydney, the country’s biggest city, authorities pleaded for people to stay at home as a major dam overflowed and a mini-tornado tore through a western suburb. Most of the coast of New South Wales (NSW) state, which is home to about a third of Australia’s 25 million people, has already seen March rainfall records broken and authorities warned the downpour was likely to continue for several days. “I hate to say this again to all our citizens of the state, but it’s not going to be an easy week for us,” NSW Premier Gladys Berejiklian told a televised briefing. “The rain may not stop till Thursday or Friday.” Officials had issued nine evacuation orders …