I don't know about any of those.
BUT:
Immortal means you live forever, but you can be killed.
Invincible means you can't be killed.
Technically immortal means you don't die. Mortal, deriving from the Latin term mors/mortis which means death, means one who dies. Immortal, having the prefix im-, which is a variant of in-, denotes a counter meaning, as in it is 'not' the term that follows it. Like how visible means you can see it, invisible means you cannot. Mortal means you can die, immortal means you don't. The term has since changed, though, and is used in separate instances between never aging and never dying.
In addition, invincible derives from an English term never used, vincible, which comes from a Latin verb, vinco (and other related nouns, adjectives, etc). Vinco means I conquer (see the 'vici' part of 'veni, vidi, vici'), and so vincible means conquerable. Invincible therefore means unable to be defeated. It is now synonymous with invulnerable though, which specifically means cannot be hurt/killed.
Sorry, I'm a Latin nerd, and I like derivatives. You're not wrong, but I like explaining things