Geometry of a dielectric in a parallel plate capacitor

Let's say we have a parallel plate capacitor, and a solid dielectric that partially fills the space between the plates.

If the dielectric is just a slab of material, with sides parallel to the plates, then I can calculate the capacitance easily. What happens if instead it is slightly tilted? Does the capacitance stay the same? And what if instead of a slab of material, the dielectric has a completely irregular shape, but occupies the same volume as before? Is the capacitance different?

In general, this will be lower than the uniform block of dielectric since air will have a lower $\varepsilon$ than the dielectric, and therefore a lower capacitance. Under certain assumptions, you can estimate the effective dielectric constant using effective medium approximations, such as Maxwell-Garnett. To be most accurate, or in cases where the air gaps are large or geometry complex, you really need to put it in a finite element model and solve it computationally.