You're not spot on, but you're close enough, so I give you right. The correct answer was simply Samantha Soul. Here's the reasoning:

An asthma mind
can help you find
the way to raise your strength - 20 Samantha Soul can be refined into Elem-Atk-J. Note: My hint about "strength" referring to the strength stat was a mistake, I just noticed. Sorry :-\

When not alone
the power stone
may help you go a length - When in a quantity of 50, the Energy Crystal refines into a Samantha Soul (helping you go a length with what was said in the first verse).

Without ado
you still can grow
the power to call forth
with greater force
the fire source
and the cold wind of north - Samantha Soul, without any refining ("without ado") can teach you to summon a stronger Ifrit and Shiva (for examples).

You're up! And also, I think this'll be my last riddle on EoFF