What are the other end products in sulfur oxoacid formation?
I am not one hundred percent certain, but I will try to give you some guidelines. There is the well known reaction of sulfur dioxide with calcium oxide.
$$\ce{SO2 + CaO -&gt; CaSO3}$$

Under aerobic conditions, this would further react with oxygen to form sulfate, since we have excess sulfur here I think it is fair to assume it will react to form thiosulfate.
$$\ce{1/8S8 + CaSO3 -&gt; CaS2O3}$$

Adding sodium sulfate is probably just a way to control/ buffer the pH during the reaction, I fail to see the actual relevance. But judging from the side reaction
$$\ce{SO2 + 1/8S8 (s) + 3H2O &lt;=&gt; S2O3^{2−} + 2 H3+O}$$
it is actually necessary to have a buffer system based on sulfate.
$$\ce{Na2SO4 + H3+O &lt;=&gt; 2Na+ + HSO4- + H2O}$$

I am not aware of any reaction of sulfur with sulfate.

In total I would write your equation like this:
$$\begin{multline}\ce{SO2 (g) + S (s) + CaO  (s) + Na2SO4 (s) -&gt;[\ce{H2O}]\\ 2Na+ (aq) + Ca^{2+} (aq) + S2O3^{2-} (aq) +  SO4^{2-} (aq)}\end{multline}$$