Since PLD contributes next to no AOE damage to begin with, there's really no reason to use STR on large AOE pulls. It will marginally increase your own damage, but cut GCDs from your healer which could've been actual AOEs.

WAR, on the other hand, has numerous abilities that scale with STR - including Vengeance, a defensive + offensive CD. There is literally no reason not to stack STR as a WAR for AOE pulls (no matter how big) as AOE DPS will go up overall and so will your self healing.

In terms of bosses, auto attacks are fluff damage that can be taken care of by a Fairy/occasional Cures or whatever it is Astro uses. They will always hit for X amount, regardless of HP pool - the only point where a larger health pool would increase your healer's DPS is the start of the fight, at the cost of your own personal DPS which would've been larger than those few GCDs lost. Even if, for some reason, your healer decides to keep you topped before going back to Cleric they'll end up losing GCDs needing to give you more Cures as well as the damage lost from yourself going full VIT. If they don't, then there was no point in the extra VIT to begin with, as it's overall a damage loss.

So. AOE pulls for PLD = full VIT, everything else = full STR. Raiding is it's own can of worms, but it sounds like we're just talking about 4mans here so I'll leave that out of this. If you're terrified that your healer might afk or let you die for the sake of their own DPS, then I guess go full VIT since your main job is to not die. I run 4mans with my boyfriend's SCH, so I never really need to worry about that, maybe DFing on your own is really that scary of an experience.