please feel free to add to these. this is what immediately came to mind from my experiences with these abilities

realworld uses for Manawall:
~Titan's landslide: negates damage and push (you can continue dps without worrying about permadeath)
~Titan's Mountain Buster: negates damage (stand there and take one just to scare the tank/healers)
~Leviathan's Dash: negates damage, you still get pushed (this is good if you're just learning the battle and haven't quite gotten the dodging down)
~Twintania's Divebombs: negates damage and push (use on 2nd set of divebombs to continue attacking big snake)
~t1 snake tailslaps: negates damage (if you want to intentionally provoke tail slaps and continue dps)
~t7 lamia tailslaps: negates severe dmg (if you are in the way of OT moving lamias to position and you want to continue dps)
~if MT dies and you happen to be 2nd on hate list

realworld uses for Manaward:
~ifrit explosion things, stand there and take 'em like a taru - if stun failed
~titan stomps, if your hp is not topped off
~t5 fireball, if you're about to eat one and your healers haven't topped you off
~t7 fireball, if you're about to eat one and your healers haven't topped you off
~anytime you're expecting magic damage and you're not at a safe hp range

etc...