If your Mesa amp has got a 16 ohm out, use that one for your 16 ohm Orange speaker cabinet. It isn't right to say "can handle", it HAS GOT a resistance of 16 ohm. I think different speaker outputs on your amp send signals with a different voltage/current proportion, so that provided power value remain the same if you use one 16 ohm cab with the 16 ohm amp's output, or if you use one 8 ohm cab with the 8 ohm amp's output, or if you use one 4 ohm cab with the 4 ohm amp's output.
You can plug your speaker cabinet into every speaker output of your amp I believe, since the resistance of your cab is higher than the minimal one requested (which is the indicate one) by the amp itself. It would have been a problem if you had a cabinet with a lower resistance plugged into a speaker out of your amp with a higher nominal output impedance (again, the indicated one): in that case the amp is not able to dissipate all the power on your speakers and you will damage internal circuitry of the amp.
If you plug your cabinet into a speaker output which has got a lower nominal impedance value, you will do a safe mismatch, but the power provided by the amp would be less than the one you could get pairing a 16/8/4 ohm cabinet respectively with the 16/8/4 ohm speaker output of your amp. I don't know if even the tone would suffer because of this...