How can I control which graph symbols or lines overlie--and therefore cover up--those for other data sets?

With Prism versions 1-3, there is no way to reorder the data sets. You'll need to remake the graph.

When you make a graph, you control the order of the symbols by when you add them to the graph. Go to the "Graphs" section, and choose to make a new graph. First choose the data set you want to be on the top. Then click "Change.. Data on graph". Add the next data set down. Each successive data set will be plotted beneath the previously added set.

Prism 4 lets you choose the front to back order of the data sets in the Order tab of the Format Symbols dialog.