What is the right way to understand the behaviour of shocking voltage?
The man gets shocked because his hand is touching the positive terminal, and his legs are touching the ground, which is connected to the negative terminal. Since the positive terminal is at a high potential relative to the ground, he gets a shock. If the load is removed, he still gets a shock.  

The bird doesn't because it's only touching the positive terminal, so there is no potential difference across it's body.  

Remember voltage is always between two points. You can't just say "this point is at 5V", you have to say "this point is at 5V relative to this point" (although people often say the former because a common reference point, like circuit ground is assumed)  

Regarding the energy being consumed part, as long as the voltage source is strong enough (i.e. has a low internal resistance) an assuming it has "infinite" capacity to keep supplying power (e.g. a mains source as opposed to a battery or capacitor) then it will supply current to many loads connected in parallel to it, without it's voltage dropping appreciably.
If it is a weak source, then it's voltage will drop if a low resistance load is connected across it - in this scenario it would be safe(r) for the man to touch it (depending on how much the voltage drops - this sort of stuff is all covered by Ohm's law, Norton and Thevenin)

Regarding edit

In an ideal situation where we assume the wires have zero resistance, then the resistance of the bird does not matter. You are right that the resistance of the bird could matter in the real world though.
We can take a look at this with a SPICE simulation. We will use your circuit above, and assume the resistance of the wire between the birds legs is 1m&Omega;. By varying the resistance of the bird we can see what would be needed to cause an appreciable current to flow through it:

Circuit:



Simulation, seeping the birds resistance from 1&Omega; to 1k&Omega;:



You can see the current through the load R1 (green trace in the bottom graph) is around 2A, and hardly changes at all.
For the bird, even with a resistance of only 1&Omega;, it only has 2mA flowing through it. At 1k&Omega;, it has 2&mu;A flowing through it (note the logarithmic graph used on the X axis due to the large variation)
In reality, unless the bird is soaking wet, and the cable it's standing on is very thin, then the above values are a long way from typical. Typical bird resistance will probably be > 1M&Omega;, and the resistance between it's legs probably less than a few &mu;&Omega;. 

Hopefully this makes some sense - it all agrees with Ohm's law, and once you get the hang of it it will seem quite natural. It might be good idea to grab something like LTSpice (the simulator used in the above examples and have a play around with it to see what happens when you change various things. Or build a circuit on a breadboard and measure with a multimeter. Also, have a good book that covers this stuff handy (see "Art of Electronics", "Practical Electronics for Inventors", etc)