House elves seem to be inordinately powerful, if they are doing it for their masters.
For example, in Harry Potter and the Deathly Hallows, after Kreacher has recounted his experiences in the sea cave: all emphasis added
‘How did you get away?’ Harry asked, and he was not surprised to hear himself whispering.
Kreacher raised his ugly head and looked at Harry with his great, bloodshot eyes. ‘Master Regulus told Kreacher to come back,’ he said.
‘I know – but how did you escape the Inferi?’
Kreacher did not seem to understand. ‘Master Regulus told Kreacher to come back,’ he repeated.
‘I know, but –’
‘Well, it’s obvious, isn’t it, Harry?’ said Ron. ‘He Disapparated!’
‘But ... you couldn’t Apparate in and out of that cave,’ said Harry, ‘otherwise Dumbledore –’
‘Elf magic isn’t like wizard’s magic, is it?’ said Ron. ‘I mean, they can Apparate and Disapparate in and out of Hogwarts when we can’t.’
To me this appears to indicate that the order of their master is greater to house elves than any wards set up to prevent disapparation, enabling them to 'do the impossible'. (I don't believe that the cave only stopped wizards disapparating and overlooked house elves, otherwise Kreacher would have simply disapparated without Regulus Black's order so that he could keep serving his master).
House elves can also perform wandless magic against wizards that are in a position of power, as in this quote (from Chapter 23 of Deathly Hallows) about Dobby disarming Narcissa Malfoy at Malfoy Mansion:
As Narcissa dragged Draco out of the way of further harm, Bellatrix sprang to her feet, her hair flying as she brandished the silver knife; but Narcissa had directed her wand at the doorway.
“Dobby!” she screamed and even Bellatrix froze. “You! You dropped the chandelier—?”
The tiny elf trotted into the room, his shaking finger pointing at his old mistress.
“You must not hurt Harry Potter,” he squeaked.
“Kill him, Cissy!” shrieked Bellatrix, but there was another loud crack, and Narcissa’s wand too flew into the air and landed on the other side of the room.
“You dirty little monkey!” bawled Bellatrix. “How dare you take a witch’s wand, how dare you defy your masters?”
“Dobby has no master!” squealed the elf. “Dobby is a free elf, and Dobby has come to save Harry Potter and his friends!”
It appears to me that these are awesomely powerful creatures that will defend their masters.
Why couldn't a house elf be given an order similar to the following:
Dobby, Voldemort is trying to kill Harry Potter and has already attempted to do so several times.
We must not let this happen.
Find Mundungus, disarm him, get the horcrux from him and destroy it (using the sword of Griffindor if necessary), then deliver Mundungus to Dumbledore for punishment.
Destroy Nagini without being caught, seen or hurt in any way.
Find the remaining horcruxes and destroy them using any manner required, while minimising damage to surroundings as much as possible.
If any horcruxes are in people, find a way to destroy the horcrux without causing the person any long-term damage.
Kill Voldemort and his willing Death Eaters, and disarm and capture the unwilling Death Eaters.
Do not get hurt in any way, do not get caught, do not get seen.
Where there limits to the power of house elves that prevented an order such as the above being used? For example, was there ever a situation where house elves were unable to fulfill an order?
Or was it just the natural habit of wizards to overlook non-human 'inferior' magical creatures such as goblins and house elves that prevented the order from being given?
Note: I do agree that to order anything/anyone into danger is wrong and unethical. But if an order could be phrased so that the house elf was in no danger, could the above order be carried out by the elf?
