Hmm, let's see...according to the thri-kreen entry in the XPH, they can take Multiattack and Multiweapon Fighting, but they don't normally get them as bonus feats. The claw attacks (or, if they have weapons there, weapon attacks) are primary weapons, and the bite is a secondary weapon. However, nothing says they have no off-hands, so all attacks made with the other three claws would count as off-hand attacks. Likewise, the text says that it can use weapons normally, and use its claws of bite as a secondary attack if it uses them after making a weapon attack.
So, according to the text for Multiweapon Fighting, a creature without that feat takes a -6 penalty for attacks with the primary hand, and -10 for attacks with all its off-hands. Remember that since gythkas are double weapons, one end counts as a one-handed weapon, and the other is light. Since three of a thri-kreen's hands are off-hands, and its using two gythkas, one off-hand is thus using a one-handed weapon, so the penalties for using multiple weapons are not reduced by 2. Hence, a thri-kreen using two gythkas, without Multiweapon Fighting, takes the entire -6 penalty to its first attack and -10 penalty to its off-hand attacks.
If he had Multiweapon Fighting, and was using a gythka and, let's say, two short swords, then he'd be in business, since all those off-hand weapons would be light. He'd just take -2 to all his attacks.
If a thri-kreen wants to use a gythka and then make claw (and/or bite) attacks, he can, but the penalties increase unless he has the relevant feats. Apply normal two-weapon fighting penalties first, and then add a -5 penalty on top of that for the natural attacks, since they'd be secondary attacks.
So, a thri-kreen using a gythka in two hands, but not Multiweapon Fighting or Multiattack, would make his first attack with the gythka at -4, and the off-hand with it at -8, and then, with the other limbs (and maybe a bite if he wanted), would make two claw attacks at -13 (the -8 for off-handed attacks plus the penalty for secondary attacks).
Now, if that same thri-kreen had Multiattack and Multiweapon Fighting, things would be a lot better. With those feats, he'd make both gythka attacks at -2, and his natural secondary attacks at -4.
(The ideas here are predicated on secondary natural weapon penalties stacking with penalties from multiple weapon attacks, which I'm not 100% sure is right. It seems to be though, from what I've seen.)
