I think that your problem is semantics, as the phrase
But since the quantum state is the combination of all the properties of the quantum object and that due to a quantum object's wave nature its position can be infinitely different,why does the PEP work?
First, it is not true that a wave nature makes the position infinitely different.
It is not a wave in spacetime first of all; and second, it is a probability amplitude. It gives you information about the likelihood of finding in particle in $dx$ region of space.
Second, a quantum state contains all information about the particle (or field) in qustion. The sentence is a combination of all properties of the quantum object makes no sense.
I emphasize: the fact that a state has all information of the system is not the same as to say that the system has all information that it can have. You are mixing these two notions.
Perhaps I can clarify this statement with an example.
If you consider a free particle, a definite mometum state is represented by $| k \rangle$. This means that
$$ P | k \rangle = \, k \, | k \rangle$$
where $P$ is the momentum operator and $k$ is some real number. Notice,
$| k \rangle$ is a vector, $P$ is an operator and $k$ is a number. There is no notion of all momenta available. It is one definite momentum $k$.
You may ask, however, what are its properties with respect to position.
To do this, you must expand $| k \rangle$ in the position basis, that is, the basis where all vectors have definite positions. Schematically,
| k \rangle = \int c(x) | x \rangle.
And it may happen that some $c(x)$ are zero, so, again, there is no notion of all different positions. In this case, it is unfortunate that no $c(x)$ vanishes. But I think you get the logic.