STR does not affect Ifrit's damage. Weapon damage and INT/Det/Crit affect all summons' damage potential. Skill speed affects Ifrit and Titan's offensive skills but it's not worth investing into for obvious reasons. Spell speed affects Garuda's.

Foe Requiem boosts Garuda, Dragon Kick blunt- debuff boosts Titan and Ifrit. Even with a MNK in the party, I'd struggle for reasons to ever use Ifrit. Ifrit's Burning Strike has an annoying delay unless you spam the command manually, and Burning Strike + autoattack is only about equal to 1 Wind Blade from Garuda. Garuda also has Contagion. Ifrit just has no point currently. Even before you get Garuda-Egi, I'd argue Emerald Carbuncle is still superior or at least equal.