Let's analyze each option:

Option A: Polarizability is the ease with which the electron cloud of an atom or ion can be distorted by an external electric field. Generally, larger ions with more diffuse electron clouds are more polarizable. In the given series, ${\mathrm{SO}}_4^{-2}$, ${\mathrm{SO}}_3^{-2}$, and ${\mathrm{S}}^{-2}$, the charge density decreases as the number of oxygen atoms increases for the same central sulfur atom, making the electron cloud more diffuse. However, comparing these, ${\mathrm{S}}^{-2}$ is a simple sulfide ion, while ${\mathrm{SO}}_3^{-2}$ and ${\mathrm{SO}}_4^{-2}$ are polyatomic oxyanions. Generally, larger anions are more polarizable. The order of size and thus polarizability is ${\mathrm{S}}^{-2}>{\mathrm{SO}}_3^{-2}>{\mathrm{SO}}_4^{-2}$. The given order ${\mathrm{SO}}_4^{-2}>{\mathrm{SO}}_3^{-2}>{\mathrm{S}}^{-2}$ is incorrect. The correct order of polarizability would be ${\mathrm{S}}^{-2}>{\mathrm{SO}}_3^{-2}>{\mathrm{SO}}_4^{-2}$.

Option B: Polarizability of anions generally increases with increasing size and decreasing electronegativity of the central atom (if applicable) or decreasing charge density. For oxyanions of the same element, as the number of oxygen atoms increases, the charge is distributed over a larger volume, which might seem to increase polarizability. However, a more significant factor is the effective nuclear charge experienced by the outermost electrons. In $\mathrm{Cl}{\mathrm{O}}_4^{-}$, $\mathrm{Cl}{\mathrm{O}}_2^{-}$, $\mathrm{Cl}{\mathrm{O}}^{-}$, and $\mathrm{C}{\mathrm{l}}^{-}$, the charge is -1 in all cases. The polarizability of simple halide ions increases down the group (${\mathrm{I}}^{-}>\mathrm{B}{\mathrm{r}}^{-}>\mathrm{C}{\mathrm{l}}^{-}>{\mathrm{F}}^{-}$). For oxyanions of the same central atom, the polarizability generally decreases as the number of oxygen atoms increases because the negative charge is more delocalized and the electron cloud becomes less diffuse. Therefore, $\mathrm{C}{\mathrm{l}}^{-}$ is the most polarizable, followed by $\mathrm{Cl}{\mathrm{O}}^{-}$, $\mathrm{Cl}{\mathrm{O}}_2^{-}$, and $\mathrm{Cl}{\mathrm{O}}_4^{-}$. The correct order of polarizability is $\mathrm{C}{\mathrm{l}}^{-}>\mathrm{Cl}{\mathrm{O}}^{-}>\mathrm{Cl}{\mathrm{O}}_2^{-}>\mathrm{Cl}{\mathrm{O}}_4^{-}$. The given order $\mathrm{Cl}{\mathrm{O}}_4^{-}>\mathrm{Cl}{\mathrm{O}}_2^{-}>\mathrm{Cl}{\mathrm{O}}^{-}>\mathrm{C}{\mathrm{l}}^{-}$ is incorrect.

Option C: Polarizing power of a cation is its ability to distort the electron cloud of an anion. It increases with increasing charge density (charge/size ratio) and pseudo-noble gas configuration (due to poor shielding by d-electrons). For cations with the same charge, polarizing power increases as the size decreases. The ionic radii are: $\mathrm{Z}{\mathrm{n}}^{2+}$ (74 pm), $\mathrm{C}{\mathrm{d}}^{2+}$ (95 pm), $\mathrm{H}{\mathrm{g}}^{2+}$ (102 pm). Therefore, the order of ionic radii is $\mathrm{Z}{\mathrm{n}}^{2+}<\mathrm{C}{\mathrm{d}}^{2+}<\mathrm{H}{\mathrm{g}}^{2+}$. Consequently, the order of polarizing power should be $\mathrm{Z}{\mathrm{n}}^{2+}>\mathrm{C}{\mathrm{d}}^{2+}>\mathrm{H}{\mathrm{g}}^{2+}$. The given order $\mathrm{H}{\mathrm{g}}^{+2}>{\mathrm{Cd}}^{+2}>{\mathrm{Zn}}^{+2}$ is incorrect.

Upon re-evaluation of the question and options, it seems there might be a misunderstanding or a trick in the question or options provided, as none of the options A, B, or C appear to be correct based on standard chemical principles. However, if the question implies that one of these is considered correct in a specific context or if there's a subtle interpretation, let's re-examine. Given that the provided correct answer is D (All are correct), there must be a specific interpretation for each option to be correct. Let's assume there's an error in my initial analysis or a non-standard interpretation is expected.

Let's re-evaluate Option A and B based on a common misconception or a specific trend. For polarizability of oxyanions, sometimes the number of oxygen atoms is considered. However, the general trend for simple ions is size. For oxyanions, the charge density and delocalization play a role. For Option A, ${\mathrm{S}}^{-2}$ is definitely more polarizable than $\mathrm{S}{\mathrm{O}}_3^{-2}$ and $\mathrm{S}{\mathrm{O}}_4^{-2}$. So A is incorrect.

For Option B, $\mathrm{C}{\mathrm{l}}^{-}$ is more polarizable than any of its oxyanions. So B is incorrect.

For Option C, the polarizing power is inversely proportional to the ionic radius for ions of the same charge. Since $\mathrm{Z}{\mathrm{n}}^{2+}$ is the smallest and $\mathrm{H}{\mathrm{g}}^{2+}$ is the largest among the three, the polarizing power order should be $\mathrm{Z}{\mathrm{n}}^{2+}>\mathrm{C}{\mathrm{d}}^{2+}>\mathrm{H}{\mathrm{g}}^{2+}$. So C is incorrect.

Given that the provided correct answer is D, there is a strong possibility that the question or the options themselves are flawed, or there is a very specific, non-obvious interpretation intended. However, based on fundamental chemical principles of polarizability and polarizing power, options A, B, and C are all incorrect.

If we are forced to choose D, it implies that all individual statements A, B, and C are considered correct. This contradicts standard chemical principles. Let's assume there's a specific context where these orders hold true, which is not generally taught. However, in a typical JEE/NEET context, these statements are incorrect.

Let's assume the question is asking for the order of polarizability of the *central atom* or some other property, but it explicitly states 'order of Polarizability' for the whole ion. For polarizing power, it's clearly defined for cations.

Revisiting Option C: Polarizing power is directly proportional to charge and inversely proportional to size. All have +2 charge. Ionic radii: $\mathrm{Z}{\mathrm{n}}^{2+}$ (74 pm), $\mathrm{C}{\mathrm{d}}^{2+}$ (95 pm), $\mathrm{H}{\mathrm{g}}^{2+}$