How do I diagnose an open circuit where several outlets are not working?
Broken wires don't trip breakers, they just cause outlets to stop working. An insta-tripping breaker means a genuine short circuit aka bolted fault. (lots of things are incorrectly called that, but this really is that).

I don't think the toaster oven had anything to do with it.  IF it had failed immediately AND it had failed "open" (outlets stopped working but breaker held), then yes.  But not in this case.

You need to check every outlet (that is now off).   Look for burning, arcing or spalling. Look on side screws, especially those sticking way out because nobody ran them down,  too-long wires sticking out of backstabs, ground wires, and sides of metal boxes. 

The most common is the bare ground wire gets too close to a hot screw or contacts a too-long backstab wire.