Assuming I have a creature, with four natural arms (or a person with extra vestigial arms — RAI I know this is unintended, but RAW it's seemingly legit) and they decided to, instead of quad-wielding one handed weapons, dual wield two handed swords. According to the rules, the offhand weapon gets 1/2 Str bonus. However two handed weapons use 1+1/2 Str bonus.
How would this strength bonus/penalty work, assuming said creature or player could not access the Double Slice feat?
The similar question Can two-hand weapons be dual-wielded by something with four arms? does not explain how the bonus damage to strength is handled.
Your issue made me think about Primary and Secondary Natural attacks, because we resolve it in the same way.
Two-Weapon fighting Rules
By RAW, you need to apply the two-weapon fighting in a strict manner.
Just like Natural attacks, you have one Primary Hand, and the others are considered off-hands. With the TWF Feat you get reduced penalties to both your hands but the concept of Primary and Off-hands stay the same
After that, just apply the rules.
No, so the full penalty applies (-6 to Primary and -10 to Off-hands without TWF, -4 to Primary and off-hands with TWF)
For strength bonus, just apply the rules as well.
Your primary hand(s) keep their usual bonus so 1.5x Strength bonus in this case, while your off-hands always have a 0.5x Strength bonus.
In the end, you're better off using 1 two-handed weapon and multiple light weapons in your additional hands.
Oh and also, you'll need the Multiweapons Fighting Feat instead of the standard TWF.