Were you reading up on guides on the internet?
I'm pretty sure they aren't needed for any quest anymore, but some of those items were used for the old meteoric gear quests. The requirements were changed a long time ago to no longer require those items(probably because it was overly difficult).
But just in case...
Emerald is a rareish drop from meteroic bosses as said, but the nonchaos aura 5* ones(both disciple and gemhoarder) can drop them as well. I believe some low level high star enemies may have a chance as well, like shiverlords, rotsmashers, flamewardens, and maybe the 6*s in dustwither.
Soul orbs are from special rare enemies, and come in various types of gems(emerald soul orb, diamond soul orb, etc). Skeletal soulwalker is the skeleton in dustwither that can drop it, and I'm pretty sure demonologist enemies can drop them as well(I know they drop diamond demonstones sometimes but I believe they usually drop soul orbs). There is an acolyte demonologist in dustwither, and a bloodgrove one in stonevale, probably more but that's all I encountered.
Skull... can't help you there, sounds familiar but I don't remember.
World - Lugh
Furyion - 191 Ice Mage
Stonelord - 100 PvP Warrior
Lavalord - 60 PvP Warrior
Keepin' it old school.
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