Usually, effects that grant natural attacks don’t grant extra limbs—so if, say, you have two different effects that gives you a bite attack, but you only have one head, you can only use one of those bite attacks in a round.
So when you get a claw attack, you don’t get another arm with which to use it. The claw goes on an existing limb. If you have no limbs left over for it, you can’t use it (or can’t use the claw or weapon in one of the existing hands).
This means the general rules of natural attacks aren’t going to help with this question. This question revolves primarily around girallon arms, an unusual case as far as these things go as it adds four claw attacks.
The thing about girallon arms is that it doesn’t just say that it grants you four claw attacks, as things similar effects granting a pair of claw attacks might. It goes through the entire process of describing how those four attacks are used—and makes no mention of limbs being needed for them. As such, girallon arms is an exception to the rule that you need limbs to make your attacks. Mechanically, it doesn’t give you four arms or four hands at all—but what it does give you is four claw attacks that don’t require their own limbs (though they do use up limbs that you do have). So all four claw attacks can be used, even with fewer than four arms or hands, but they can be used only for the claw attacks described in girallon arms.
It would be nice if Magic of Incarnum came out and said this explicitly, instead of requiring the reader to make these connections. But what it does do is set up the expectation of how it’s supposed to work in the italicized “fluff text” above the actual effect of the soulmeld:
Incarnum forms two additional, powerful arms that spring out from your ribs. These spirit arms mirror the movements of your real arms. All four of your arms are tipped with long claws that no longer seem ghostly, but quite real—and quite sharp.
So girallon arms gives you the two additional limbs you need to use the extra claw attacks. However, these arms are “spirit” and “ghostly” aside from the claws themselves, and in any event, mirror the movements of your real arms (implying an inability to perform independent actions). So it both seems the likely intent, and more keeping with the themes of the class, not to allow it. Personally, because I rather like the themes of the totemist class and because totemist is right around the right level of power for my games, I would not allow it.
You can, of course, use your real limbs to wield weapons, replacing up to two of the claw attacks from girallon arms in this fashion. The remaining two claw attacks, performed with the spirit arms, would be secondary attacks at the end of your full-attack.