How do Catholics traditionally understand the divine omnipotence?
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By intrinsically impossible, Aquinas means that the thing meant to be brought about is logically impossible, ie it entails contradiction, as Rob has stated. Before Aquinas, Augustine gave us more or less the same answer in The City of God
we do not put the life of God or the foreknowledge of God under necessity if we should say that it is necessary that God should live forever, and foreknow all things; as neither is His power diminished when we say that He cannot die or fall into error — for this is in such a way impossible to Him, that if it were possible for Him, He would be of less power. But assuredly He is rightly called omnipotent, though He can neither die nor fall into error. For He is called omnipotent on account of His doing what He wills, not on account of His suffering what He wills not; for if that should befall Him, He would by no means be omnipotent. Wherefore, He cannot do some things for the very reason that He is omnipotent.
In context, Augustine is making a different point here, but given that he wrote this, he would likely agree with Aquinas. Here, we must say that there are some things that God cannot do because He is omnipotent, and to do them would entail that He is not omnipotent. EG, if He could create a boulder so large that He could not lift it, this would entail He is not omnipotent (He lacks the power to move a particular boulder). Hence, he cannot make such a boulder precisely because such a boulder cannot exist (He is omnipotent; any boulder which can exist can be moved by Him).
Against Faustus, Augustine says: "Whosoever says, If God is almighty, let Him make what is done as if it were not done, does not see that this is to say: If God is almighty let Him effect that what is true, by the very fact that it is true, be false." (Auquinas refers to this in his question concerning the power of God) This is a more general statement that God cannot produce contradiction. Take any contradiction you can think of, eg, a square circle. We can correctly define a circle as "a particular shape which is not a square" and correctly define a square as "a particular shape which is not a circle." These definitions, while incomplete, accord with reality, and they show us more plainly the contradiction. Applying what Augustine says here, someone who says that God can make a square circle says that God can "effect that what is true, by the very fact that it is true, be false." That is, He can cause a shape S for which it is true that S is a square AND false that S is a square (as square, the square circle is truly square; as circle, it is "not a square," thus falsely called a square).
Now in both of these rebuttals, Augustine seems to be answering, once directly and once indirectly, the charge of those who ask such questions as "Can God create a boulder so large even He cannot lift it." Augustine, clearly, thinks such questions are silly. They rhetorically ask something absurd, something which, if it were more plainly defined, would be apprehended as ridiculous by even those with the darkest intellects. This view of Augustine has been the standard response regarding omnipotence challenged in this way since his lifetime, for all Catholics and pretty much all Christian apologists, both before and after Aquinas.
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