Been a while since I last read LoTR but I remember Legolas would sometimes take the arrows he loosed from the enemies' body. Obviously he has a limited supply and there are times where he couldn't retrieve some (enemies are too far high up or below, arrows "might" be damaged but they're Elvish so probably not etc).
Did he ever take and use Goblin/Orkish arrows or would that have been too frowned up as those arrows are used against the Free Races?
Yes, he did.
While it's left vague in some places, it's quite clear that after the Breaking of the Fellowship he took Orc arrows (source: The Two Towers, the Departure of Boromir):
'And I,' said Legolas, 'will take all the arrows that I can find, for my quiver is empty.' He searched in the pile and on the ground about and found not a few that were undamaged and longer in the shaft than such arrows as the Orcs were accustomed to use. He looked at them closely.
Only Orcs took part in the attack on the Fellowship, so therefore these can only have been Orc arrows.
