How can I tell (easily) if my power supply is regulated/switched or unregulated/nonregulated?
Using your voltmeter, just measure the output of the wall-wart without any load.  You can generally stick one probe into the middle of the connector, and hold the other against the outside.  With a few exceptions, the middle is positive, so use the red lead there, and use the black lead on the outside shell.

Regulated supplies, without any load, should measure very close to the target voltage of 12v.  Unregulated supplies will generally have a no-load voltage anywhere from a couple of volts to several volts higher.  If they measured 12v without any load, they would have no headroom to take care of the drop due to the load.