It seems mostly correct except for two-weapon fighting and double slice. Going to large the eidolon goes from 15 to 13 dex. He can get them before going large but loses their benefit afterwards. TWF gets replaced by multiweapon fighting but double slice still needs the 15 dex.
I get this for all the attacks :
Attack Bonus : 18 = 7(BAB) + 11 (str) + 1(weapon) -1 (size) => 16(main) /12(sec)
natural : 15 = 7(BAB) + 11 (str) -1 (size) -2(secondary)
damage bonus : 11(str) +1(weapon) / 5(str) +1(weapon)
natural damage bonus : 5(str)
Sword 1 (-2): +16/+11 - 2d8+12
Swords 2-6: +12 - 2d8+6
Claws 1-2: +15 - 1d6+5 dmg => you can't use the claw of a hand wielding a sword.
Wings 1-2: +15 - 1d8+5 dmg
Tail : +15 - 1d8+5 dmg
If all the blades connects, that would be 17d8 + 66 ~ 142. Nice but unlikely, the attack bonus is rather weak. An appropriate CR would have around 24 AC, and probably some damage resistance, so maybe half will connect and most of the damage will be reduced. You should consider getting a bastard sword for each type of damage reduction, and versatile weapon.
Getting weapon focus with the feat intended for double slice might be a good idea, and focus on crippling the opposition AC to help your eidolon. Protect him well, he has few HP and crappy saves.
At 9th level an Eidolon's total attacks is 5, so I don't understand where the extra attacks are coming from... I find it hard to believe - and would never rule - that his total number of attacks were 5 plus as many weapons as you could buy arms for.
That ruling specifies synthesists. Exactly how much it applies to non-synthesists could be debated by a crankier GM (synthesists breaking the action economy less anyway).
At 9th level an Eidolon's total attacks is 5, so I don't understand where the extra attacks are coming from... I find it hard to believe - and would never rule - that his total number of attacks were 5 plus as many weapons as you could buy arms for.
It does work that way, although if you fill an Eidolon to the brim with weapons I'd argue that it comes out weaker in the end. Too expensive to make everything magical, hit penalties kinda suck and you lose out on any sort of defense.
But what I do think is pretty nasty is providing it with a single large weapon. Give a set of arms to use for a single additional weapon after the Eidolon gets Multiattack. Burn a feat for proficency rather then evolutions. After it's summoned hand it a large Greatsword, preferably at least +1. The Eidolon gets 5 natural attacks plus a sword that works with iteratives, and only a few evolution points were spent freeing up other uses. With Multiattack everything is being made at only a -2 penalty.
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The normal penalty is -6 main hand, -10 off hand. With Multiweapon Fighting it becomes -4 main hand, -4 off hand. You can reduce it another two by using light off hand weapons. It's not a function of the feat. It's just how two-weapon fighting works. "Off hand weapon is light" is its own entry in the table.
If your full attack bonus with the bastard sword is 18, then if you're multiweapon fighting, it's 14. The offhand weapons will be the same.
+14/+9 main hand
+14 off hand
If you were using all shortswords, it'd be:
+16/+11 main hand
+16 off hand
There is no evolution named wings - they are part of flight evolution.
Penalty to attack rolls and bonus to damage applies to all attacks.
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@Gjorbjond
http://www.d20pfsrd.com/feats/combat-feats/multiweapon-fighting-combatSRD says -2 with main, -6 with all off- doesn't say anything about light off hand weapons (I checked =,= )
What you forgot to check is the normal rules for fighting with multiple weapons, which are covered under the two-weapon fighting feat.
The reduction in attack penalty for using a light weapon in your off hand is not a function of a specific feat, it always applies.
Normal: If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon. When fighting in this way you suffer a –6 penalty with your regular attack or attacks with your primary hand and a –10 penalty to the attack with your off hand. If your off-hand weapon is light, the penalties are reduced by 2 each. An unarmed strike is always considered light.
Feel free to enjoy full BAB interative with a two-handed weapon as your primary and put a light weapon in each of your off hands.