Immortal is capable of being a status effect, and can't be lobotomized, so theoretically that could stack with the others. Momentum behaves the same way - like Phase Dragon, Sapphire Charger has the "momentum" active ability which generates the momentum status upon summoning. Lobotomize of course removes both, but Liquid Shadow only removes the "momentum active ability, not the status.
(An aside: Charger/LS deck sounds like a pretty neat idea!)
This means that "immortal" can theoretically coexist with another active ability, given a small amount of recoding. The "death-devourer" ability on the "rigth" hand is a passive (you can't lobotomize a Devourer's Devour, only its Burrow). Even with all that, though, you're left with two actives on each card - Plague/Scavenger and Pandemonium/Scavenger.
Pandemonium on a stick is also probably not a great idea, especially on an immortal creature.
EDIT: Ninja'd by the OP there... I'm still not sure plague on a stick is a great idea. The only creature poison ingame is a plain ol' single-target Infection, which requires duo cards (Parasite or Toadfish).