"What is the difference between using self-raising flour and plain flour with a raising agent, such as baking soda? Why do recipes use plain flour with soda when clearly self-raising flour would do the job?"
Self-raising flour has a specific ratio of flour to baking powder. To replicate self-raising flour the proportion is approximately 1 tsp baking powder: 150gm (1 cup) of plain flour. However, many recipes require a different proportion of baking powder to flour in order to achieve the desired leavening. This is when the recipe will call for plain flour and baking powder as separate ingredients. For example, a banana cake, being a heavier batter, will often require more baking powder to rise than is present in self-raising flour. It may require, let's say, 1 cup of plain flour and 2½ teaspoons baking powder, and hence will call for plain flour and baking powder. For this reason, it's not advisable to simply substitute self-raising flour or you may find yourself with a less-than-desirable result. The other reason that can come into play with publications which cater to an international market is simply that self-raising flour isn't available in some countries (the US is a case in point), so providing a plain flour/baking powder solution means the recipe can be cooked by people who don't live in Australia.
Strong plain flour has a higher gluten content than plain flour, which makes it suitable for things like pasta, dough and bread-making, which require the gluten component of the flour to be "worked" in order to provide the necessary structure. Strong flour is also sometimes called OO, bread or pizza flour. It's not ideal for cakes, biscuits or pastries which need a tender crumb and crumble texture.