Christian tradition has it that Judas the traitor was hanged on an elder tree so this might explain the association with death.
I'm a practical witch and I believe that most folklore has its roots in practical answers. My guess would be that knowing elder is an unpleasant wood to burn, giving off little heat and a lot of quite smelly smoke it became a wood to avoid burning. I would imagine it was rejected as a source of firewood and the myths sprang from the reluctance of people to burn it. It is also a very quick burner so possibly there was a concern of the fire spreading too quickly for safety and this was also a factor in shunning it.
Elder is also a very useful tree with almost all parts of it having a purpose. The berries, the flowers and the leaves are all edible and even the bark can be used for medicinal cures. With elder trees providing so much bounty to the communities of old it is unsurprising that cutting them down for use of firewood was frowned upon.
Image http://www.sxc.hu/photo/1402779 (Ayla87)