I equipped two of my dwellers with a minigun and gatling laser. Raiders attacked, and I was excited to see how much those two weapons would fare. However the issue at hand is the dwellers didnt shot at all. They just ran back and forward while taking damage. They never fired'em.

Am I missing something? Does the dwellers need more str?

It just happens sometimes. A bug. I actually just had it happen myself today: dude with a tuned gatling waiting to greet the raiders when they hit the vault door room, and they just ran right past him. Idiot stood there looking dumbfounded. Had to chase them down the hall.

I can't say I've seen the bug that Greslin mentioned, but I do know it's a "normal" graphical bug for it to not show the wepons being fired during a raider/deathclaw/molerat/radroach attack. Your dwellers will still deal damage to the attackers at the normal rate for the weapons they have, it just happens invisibly while they run around like chickens with their heads cut off. My theory is that it does this because some weapons have a minimum distance at which their firing animation will play, and if the attackers are right on top of your dweller, your dweller will try to relocate to a position further away. Sometimes (frequently with weapons like the minigun), there's nowhere for them to go that satisfies this requirement, and they never "fire."

I got a fatman in a lunchbox and so far have only seen it actually fire once but it still seems to do damage even while said dweller is running around durring an attack.

Even under optimal conditions the larger weapons have a large cool down between shots. Gatling guns even have a setup time. Then you have the AI letting your dweller run around messing up the firing sequence causing the weapon to not fire at all. Applied DPS is independent from anything displayed.

It also seems to me that the game will only animate so many weapons firing in the same room, so you may only see 4/6 weapons firing in a single room. I'm guessing it is to avoid slowdown

I've noticed that the best place to see weapons fired is the Vault Entrance room, it is the same size as a four person room, but only two dwellers can be in it. I currently have a Fatman and an Enhanced Missile Launcher in there, and I regularly see the animations. My next room is a six person Nuka Cola factory stocked with six hardened flame throwers, those guys just run around the whole time, but two Deathclaws are always dead by the time the third one is ready to hit the next room so they are taking damage the whole time.

It's just an animation, your dwellers are fighting the raiders, even if you see your dwellers walking left and right, it still deals damage