Toroidal Core Calculation
Saturation of the core is a major limiting factor that may dictate more turns on the primary. More turns = much more primary inductance (L is proportional to turns squared) and this means a lower magnetization current for a given sinusoidal voltage on the primary.

Lower mag current means lower saturation (note that saturation is NOT due to VA being passed through the transformer). 

So, a smaller core needs more turns to avoid saturation at a given primary voltage and, of course, more turns means more copper losses. This is why bigger cores are better for VA ratings - not only can you use fewer turns (to obtain the same primary inductance) but the H field is smaller. H is ampere-turns per metre where the "per metre" part is the nominal average length around the toroid (or core).

Yes, for a bigger core, each turn is a bit longer (more resistance losses) but the net effect is a decrease in copper loss and this means more VA can pass through the core.

But the problem here is that you know nothing about the core material hence you cannot predict where on the BH curve saturation might become a problem. This means you cannot safely predict magnetization current and you don't really know how much inductance the core produces per turn (because permeability of the core is unknown).

All this leads me to say is that if I were in your position I'd throw it in the garbage and buy something that that was defined in data sheets.