As well as the Rüppell's Vulture at 11,000m (36,000'), there's also a record of a goose colliding with a jumbo jet at 10,700m (35,000') over the US east coast, and a flock of 30 swans (presumed Whoopers) at 8,200m (27,000') between Iceland and Ireland.
Seems the goose and the swans were using northerly jetstream winds to speed up their migration - the swans case was studied carefully, discovering that they were using the 110mph northerly jetstream winds in the lower stratosphere to cut their journey time form Iceland to Ireland, from over 24 hours, to just 7 hours. The conditions at that altitude are severe, to say the least: -50°C, and only 40% of sea level atmospheric pressure. Take a person to that altitude straight from sea level, and they'd be dead of anoxia within a few minutes.
Given those condition, I don't like to think what it was like at the altitudes the vulture and goose were at, probably less than a third of sea level pressure. The goose was presumably also on migration, but what the vulture was doing that high, I can't think. That high up (nearly 7 miles), it I doubt it would even be able to see a dead elephant!
As for small birds, flocks of migrating passerines have been radar-tracked as high as 7,000m (23,000'), though that is exceptional, usually they fly much lower. Still high enough to kill a man who hasn't had prolonged high altitude fitness training, yet these birds can do it by going up straight from sea level.
Michael