It's often said, and many believe, that god is omnipotent, omnipresent and omniscient... which begs one question...
Does god know he can make a rock so big he can't move it?
I prefer the version about a taco.
"Can God create a taco so hot that he can't eat it?"
Hebrews 6:18 suggests an approach to this question by pointing out that there are things in which it is impossible for God to lie. The passage says,
When God made the promise to Abraham, since he had no one greater by whom to swear, he swore by himself, and said, I will indeed bless you and multiply you. And so, after patient waiting, he obtained the promise. Human beings swear by someone greater than themselves; for them an oath serves as a guarantee and puts an end to all argument. So when God wanted to give the heirs of his promise an even clearer demonstration of the immutability of his purpose, he intervened with an oath, so that by two immutable things, in which it was impossible for God to lie, we who have taken refuge might be strongly encouraged to hold fast to the hope that lies before us. This we have as an anchor of the soul, sure and firm, which reaches into the interior behind the veil, where Jesus has entered on our behalf as forerunner, becoming high priest forever according to the order of Melchizedek.
(Hebrews 6:13-20)
You may object to this use of scripture as evidence for the proposition that I am about to state; that is for you to decide.
God cannot do anything that is impossible to do.
One example of an impossible thing is to make a triangle that has exactly two sides. Other examples will occur to the reader.
A materialist might formulate an answer thus:
Basing the answer on the fundamental equivelence of mass and energy (through the equation e = m * C^2),
A universe in which there exists such a thing as an irresistible force is, by definition, a universe which cannot also contain an immovable object. And a universe which contains an immovable object cannot, by definition, also contain an irresistible force. So the question is essentially meaningless: either the force is irresistible or the object is immovable, but not both.
Thus, this question appears to be a case of the fallacy of the pseudo-question.