I have a Half Elf Oracle Arcane Lore Keeper that is taking Eldritch Heritage (arcane). Would I be able to take the extra spell known as a Favored Class Option (as a Human sorcerer) from either the oracle or the sorcerer/wizard spell list? Would it be one level lower than what I could cast from the arcane spell list?
No. Eldritch Heritage in no way makes you a sorcerer or a wizard, even the arcane bloodline.
So it wouldn't even be allowed if my second favored class were sorcerer?
Right, favored class just means that if and when you take an actual level in that class you get a cookie.
So what about the expanded arcana feat? Would I be able to take extra sorcerer spells if I previously had the eldritch heritage feat?
Nope, EH doesn't give you spellcasting, so you don't have the sorc/wizard list to draw from.
Basically what you're looking for is an Amateur Sorcerer feat, and there just isn't one. (Well, there's variant multiclassing, but VMC Sorcerer only gets bloodline powers and a feat, not spellcasting.)
I have a Half Elf Oracle Arcane Lore Keeper that is taking Eldritch Heritage (arcane). Would I be able to take the extra spell known as a Favored Class Option (as a Human sorcerer) from either the oracle or the sorcerer/wizard spell list? Would it be one level lower than what I could cast from the arcane spell list?
Unless a class feature (specifically a class feature) is adding a spell to your Spells Known or something else specifically adds a spell to your class spell list (Samsaran Mystic Past Life), you cannot cast any spells not already on your class spell list. Eldritch Heritage does not make you a sorcerer. And to nip another probable problem in the bud: New Arcana taken through the Eldritch Heritage line will NOT give you access to Sor/Wiz spells. Unless something specifically adds a spell to your class spell list, or your class is adding spells to your class spell list (like Oracle mystery spells), you don't get to cast it.
New Spells Known: If I gain the ability to add a spell that is not on my spell list to my list of spells known, without adding it to my spell list, can I cast it?
No. Adding a spell to your list of spells known does not add it to the spell list of that class unless they are added by a class feature of that same class. For example, sorcerers add their bloodline spells to their sorcerer spell list and oracles add their mystery spells to their oracle spell list. The spell slots of a class can only be used to cast spells that appear on the spell list of that class.