What happens if I use the DC Voltage setting on an AC line? What about the reverse?
As long as the meter's voltage range is initially set to at least the highest that can be there, you won't damage the meter, especially if you make just a momentary initial connection to see what the meter does.  What happens with the readings will depend in part on the type of meter, whether it auto-senses polarity, whether it is auto-ranging, and whether it has a digital display.

For example, a mechanical meter with a needle and scale will "peg" the needle below zero if the meter is set to DC, and you measure a DC voltage with the polarity reversed.  It will peg the needle at the end of the scale if the voltage is higher than the setting, either AC or DC with the correct polarity.

With a digital meter that auto-senses polarity, you will get a negative accurate reading if you have a DC setting and measure DC with the polarity reversed.  It will show zero or an error if the polarity is reversed and it isn't auto-sensing.

AC will display as zero voltage on a DC setting, regardless of the polarity.  Reversing the leads and still reading zero will distinguish this from DC with reversed polarity if the meter displays zero for reversed polarity DC.

Measuring DC on an AC setting will depend on the meter.  The meter rectifies AC to turn it into DC for a reading.  DC with polarity in reverse of the rectifier will read zero.  Reversing the leads should give you a reading, but it is likely to be inaccurate because the meter is scaled for the rectified voltage.

The combination of AC/DC settings and polarity reversal should allow you to figure out whether the source is DC or AC.