Auroras are like snipers. I put some flares (about 7 flares for every 5 aurora) in my armies to soak up damage and to hurt anything that tries to rush them. They're dirt cheap so who cares when they die - at least the aurora wasn't hit. When combined with an attack-move order the auroras will often survive to fight another day while the flares will take the biggest chunk of the damage.
Mantises are like an enveloping swarm - they're good for punishing an enemy who over extends, they can cut off reinforcements and hit the artillery from the side - they're good for flanking and kiting - if you have 5 mantises shooting 3 strikers, the mantis should trade favorably even if there's 15 strikers behind them. Ebb and flow like waves on the shore, draw them out and strike when they're weak and disorganized.
Strikers are like a clenched fist - they can punch straight through any enemy line and march right through to the artillery. They can be an impassible wall or a spear thrust through the gut - they are indomitable. And slow. And short range. And easily outmaneuvered / kited. They are best launched like a bullet from a gun, straight for the heart of your foe.
I don't play aliens so idk about the Thaam