But doesnt Harry say at start of 6 to Dumbeldore that he wants to kill as many Death Eaters as possible in the process of trying to take down Voldemort?
It seems to me that in a battle situation - eg, Battle of Dept of Myst in 5, or Battle of Hogwarts in 7 - they'd certainly duel to kill. M McGonagall says to Slughorn that if the Slytherins attempt to sabotage their fight against the Death Eaters, then we will 'duel to kill.'
Dolohov, Lucius Malfoy,B Lestrange and co in Book 5 are completely willing and prepared to kill anyone in their way, so for an Order memeber to use a similar spell in that situation, would be self defense. Also remember that Sirius and Bellatrix are dueling around the dais with the veil - if Sirius knows that if you knock someone out behind the veil, then they die, well, then mightn't he be trying to kill B Lestrange? It's a possibility.
It's possible that they would prefer to send captured Death Eaters to Azkaban, however. (Although Dumbledore thinks the dementors' very presence in Azkaban is cruel and unusual punishment - not sure where he says this but he does! I think there's a line in 3 - Mr Weasley says he, like Dumbeldore, doesnt like the dementors, but sometimes you have to 'join forces with those you'd rather avoid' in extreme situations, such as, at that time, capturing the supposed mass murderer S Black.
Oh, and at end of book 4, Dumbledore tells Fudge he thinks the dementors wil soon rejoin Voldemort. So he isnt keen on them for that reason as well.
Snape could not kill a Death Eater because then he would be revealed as a spy and have to either go into hiding or be killed by Voldemort. Probably he'd be killed even if he went into hiding. So he's a special case. Other than that, however, it seems that Order members will use Avada Kedavra in battle situations.