Sturbanger's not fat... No seriously. I have a suspicion saying that his weapon doesn't have a hitbox. Make him as small as possible, his core allows it. Anywho, I'd build him by using his missiles as a main, a secondary main weapon for closer encounters and I'm serious on this, hammer.
Hammer works. No need for high STR as STR doesn't effect knockback.
But the more popular Sturbanger suggestions would yeild in use of Psycho Formula HD2 to "lead" the missiles.
Contrary to his store build, he shouldn't be used as an alpha striker.
I have nothing for Toybox. I did get a HEAT from RO cubes. His AM never seems to hit and his BD is too slow for PvE. BAZ, on the other hand... Yet, this topic isn't BAZ builds. I can't help with you Toy.
Edit: Oops. I left out a few important parts of Sturbanger. His missiles are truly his main weapon. Near-endless supply of ammo, quick enough to be used in most situations, a long firing duration, etc. USE IT.
Most thing on (at least) Stock Sturbanger implies that he's a defensive bot. In this metagame, he's not. Get as much mobility as possible (whatever works, 2 FLY and 2 WLK core). Use aggressively, I'd assume.
As for shooting, Stur missiles have a tiny sweetspot. The sweetspot is outside of his blindspot and inside his range. You can make this sweetspot temporarily larger by using a Railgun or other long range weapons (increase range), or by using a Psygun like Formula HD2 (decrease blindspot). This is also where mobility helps, keep things in the sweetspot. Got lock but missiles not hitting? Retreat or get more distance. No lock? Get closer.
As for what to shoot at, AIRs. AIRs, AIRs, AIRs, AIRs, AIRs, AIRs, AIRs! Ignoring Slutraph.
After that wall of text, Get hypershot. And lots of it.