Now how do you even propose the character would wield a weapon with four hands? As it is, one-handed and two-handed weapons can't be used with more than two hands. Period. At best a 4-armed character will be wielding two weapons that are each two-handed. With their Strength penalty and Small size, that's still not going to be awesome damage.
Examples:
1st-level human fighter wields a greatsword. Str 18. Weapon Focus, Power Attack, and Cleave for initial feats. Always uses PA since his WF feat balances out the penalty. So each round he attacks once for 2d6+8 damage, with +5 on the attack roll, whether it's a standard attack or full attack or charge or attack of opportunity or whatever.
1st-level Quan-Ri fighter wields two Small greatswords. Str 16. Multi-Weapon Fighting and Power Attack feats. Always uses PA just because he likes to pretend that he's as good as the human fighter. On rounds where he can full-attack, he gets off two strikes at +0 to the attack roll (that's right; +3 Str, +1 size, +1 BAB, -1 PA, -4 for two weapons with neither being light). The Quan-Ri deals 1d8+6 damage per hit with the primary hand, 1d8+3 damage with the off-hand. So on a full-attack, he deals at best 2d8+9 damage, mildly better than the human fighter, but at a much reduced attack bonus.
Perhaps a better comparison in this context. 1st-level human fighter wielding two bastard swords. Str 18. Exotic Weapon Proficiency, Two-Weapon Fighting, Power Attack. On a full-attack, gets two attacks at +0 each, deals 1d10+6 damage with the primary hand and 1d10+4 damage with the off-hand. Total of 2d10+10 potential damage. Slightly superior to the Quan-Ri. Spent the human bonus feat on EWP to match and exceed the Quan-Ri's own racial benefit of four arms.
Final comparison..... 1st-level Quan-Ri fighter wields four Small bastard swords. Str 16. Multi-Weapon Fighting and Exotic Weapon Proficiency feats. On a full-attack action, he gets four attacks at +1 each, dealing 1d8+3 damage with the primary hand and 1d8+1 damage with each of the three off-hands. Total potential of 4d8+6 damage. Now this is the only terrible scenario.
Taking that last scenario into consideration..... The racial Strength penalty should probably be -6, or -4 with an additional -2 Dexterity penalty. This would make it very difficult to get the necessary Str and Dex scores to acquire Multi-Weapon Fighting, Power Attack, Exotic Weapon Proficiency (Bastard Sword or Dwarven Waraxe), and so on. If we went with -6 Strength instead of -2..... Then the first scenario would have the Quan-Ri taking Weapon Focus instead of Power Attack (as their Str would be insufficient at 12), getting two attacks at +2 each for 1d8+1 and 1d8 damage, for a total of 2d8+1 damage, quite reasonable considering the feats and penalties involved (as shown by the example human using two bastard swords; even two longswords or perhaps two shortswords would out-do the Quan-Ri in this case). With -6 Str instead of -2, the later (aka worst case) scenario would have the Quan-Ri wielding four Small longswords, with Str 12 and Weapon Focus, getting 4 attacks at +0 each (+1 size, +1 Str, +1 BAB, +1 WF), each dealing 1d6 damage (though +1 damage for the primary hand). So 4d6+1 damage (avg. 15, max. 25) compared to a human doing 2d10+10 (avg. 21, max. 30). This would make the race quite fair for LA +0 (probably even a bit underpowered considering their Cha penalty and the crippling Str penalty for those PCs who don't invest a base score of 18 into Str to get 12).
