Step 1: Write the reaction of each compound with $\text{HCl$.}
The reaction of salts with a strong acid like $\text{HCl}$ displaces the weaker acid from its salt.
(A) $\text{Na}_2\text{CO}_3$: Sodium carbonate reacts with $\text{HCl}$ to release carbonic acid, which decomposes to water and carbon dioxide.
\[
\text{Na}_2\text{CO}_3 + 2\text{HCl} \to 2\text{NaCl} + \text{H}_2\text{O} + \text{CO}_2(\text{g}) \uparrow
\]
Oxide products: $\text{H}_2\text{O}$ and $\text{CO}_2$. (2 oxides)
(B) $\text{NaNO}_2$: Sodium nitrite reacts with $\text{HCl}$ to form nitrous acid, which is unstable and decomposes into nitric oxide ($\text{NO}$), nitrogen dioxide ($\text{NO}_2$), and water.
\[
\text{NaNO}_2 + \text{HCl} \to \text{HNO}_2 + \text{NaCl}.
\]
\[
3\text{HNO}_2 \to \text{HNO}_3 + 2\text{NO}(\text{g}) + \text{H}_2\text{O}.
\]
Upon exposure to air, $\text{NO}$ oxidizes to $\text{NO}_2$.
\[
2\text{NO} + \text{O}_2 \to 2\text{NO}_2.
\]
The oxides that are formed are $\text{NO}, \text{NO}_2$ (and $\text{H}_2\text{O}$). (2 nitrogen oxides)
The reaction with $\text{NaNO}_2$ yields the maximum variety of oxides of Nitrogen upon further decomposition and reaction ($\text{NO}, \text{NO}_2, \text{N}_2\text{O}_3, \text{N}_2\text{O}$). The question asks for the greatest number of oxides. Let's stick to the initial decomposition. The products are $\text{NO}$ and $\text{H}_2\text{O}$. $\text{NO}$ quickly converts to $\text{NO}_2$. Total oxides: $\text{H}_2\text{O}, \text{NO}, \text{NO}_2$. (3 oxides)
(C) $\text{Na}_2\text{SO}_3$: Sodium sulfite reacts with $\text{HCl}$ to release sulfurous acid, which decomposes to water and sulfur dioxide.
\[
\text{Na}_2\text{SO}_3 + 2\text{HCl} \to 2\text{NaCl} + \text{H}_2\text{O} + \text{SO}_2(\text{g}) \uparrow
\]
Oxide products: $\text{H}_2\text{O}$ and $\text{SO}_2$. (2 oxides)
(D) $\text{NaHCO}_3$: Sodium bicarbonate reacts with $\text{HCl}$ to release carbonic acid, which decomposes to water and carbon dioxide.
\[
\text{NaHCO}_3 + \text{HCl} \to \text{NaCl} + \text{H}_2\text{O} + \text{CO}_2(\text{g}) \uparrow
\]
Oxide products: $\text{H}_2\text{O}$ and $\text{CO}_2$. (2 oxides)
Step 4: Conclude the final answer.
Reaction with $\text{NaNO}_2$ is the most complex, yielding $\text{NO}$ and $\text{NO}_2$ (and $\text{H}_2\text{O}$) upon decomposition, thus forming a greater number of different oxides ($\text{H}_2\text{O}, \text{NO}, \text{NO}_2$) compared to the others which form two oxides ($\text{H}_2\text{O}, \text{XO}_2$).