It's always seemed to me that the question is not meaningful. If a force comes against an object, one of two things happens:
1. The object moves.
2. The object does not move.
I can't think of any alternatives to these two options.
If (1) is true, then the object was never immovable.
If (2) is true, then the force was never irresistable.
Therefore, the posited interaction could never happen. You could not have both an immovable object AND an irresistable force, even in theory. One or the other, maybe (in theory), but not both.
By the way, several here have indicated that a force will cause any object to move, even if so slightly as to be undetectable. Maybe so, but I don't see that as being relevant. Either the object moves or not. The degree of movement makes no difference.