Leka is the verb for the action of playing itself. It doesn't need an object. Spela usually requires an object indeed. Ex.: Jag spelar fotboll, volleyboll, dataspel. Ex.2: Jag leker / Jag leker med dig / Jag leker ensam. Tala and prata are synonyms and you can use them in the same way, even though in my experience it looks like Swedes use more prata than tala in speeches. Hope this will be helpful :)

Talar and pratar are like "to talk" and "to speak", we use it pretty much the same way, although pratar is used more frequently in everyday life. Leka is, like someone said, almost always used when you talk about children, who play (leker) with toys or with each other. Spela is used when talking about games, for example.