A soapie is normally a tv show (normally drama). It's often on tv five days a week and can run for years and years. Australia has quite a few of them. Most people think they're pretty bad and boring.
Having a "bun in the oven" means you're pregnant. Bread baking in an oven rises (in other words, it gets bigger, like the stomach of a pregnant woman - hence "bun in the oven"). I'm Australian, it's quite a common saying here. It's used very informally and is considered slang.