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If there isn't a VA rating on the label or published in a reliable source, then you have to guess.  There are several clues that can be used:<ol>

<li>Look at the size of the primary wires.  That gives you an upper bound on the primary current.  You know this is meant for 220-240 V systems, so between these you get an upper bound on the input power.

This is so unreliable as to not be worth bothering with for a "small" transformer.  Your transformer looks big enough to be meant to handle enough power, and therefore input current, so that the wire won't be grossly oversized.

<li>Put a fixed sine wave in at the rated frequency (50 Hz in your case) and see what comes out the secondary open-loop.  Do not give it the full rated input voltage.  In this case, I'd use a variac to drive the primary without about 50 V.  Measuring the open-circuit output voltage then gives you the transformer ratio.

<li>Knowing the secondary voltage from #2, use the method from #1 to get an upper limit of power.

<li>Use the setup from #2 and see what the output short-circuit current is.  I'd start with the variac at 0, then slowly crank it up to get a meaningful output current, but at well below intended power.  The transformer should be able to handle 10% of the rated input voltage with the secondary shorted indefinitely.

By measuring the open-circuit voltage and the short-circuit current, you can get an idea of the impedance of the whole unit as seen looking into the secondary.  The maximum possible output power is half the open-circuit voltage times the short-circuit current <i>at the full rated input voltage</i>.  That is a guaranteed not to exceed value, and not likely the intended operating power.

<li>Take a guess on power dissipation based on size, then work backwards to intended operating power based on a guess of efficiency.

It's hard to get the size from your picture, but if it's fist-sized, then it can probably handle 10 W dissipation without damage.  You can actually try different dissipations with the variac setup and shorted secondary to see how much power gets it too hot.  Remember that the windings inside will be hotter than the outside of the bulk iron.  I wouldn't let the outside get hotter than what you can hold your hand on indefinitely.

Your transformer doesn't look particularly high tech.  It has the look of cost being a higher priority than efficiency.  I'd guess 80% efficiency at best, probably lower.

<li>Consider how this transformer was used, if you have that.  Did it come from a 1960s television (an old TV transformer would have multiple secondaries, this is an example only)?  Any such appliance would have a maximum line current or power shown on the nameplate by the line cord entrance.  Especially for a consumer item that was designed for low price, the transformer will be just barely able to handle the maximum input power.

Even if the specific appliance isn't available anymore, a 1960 TV is unlikely to draw more than 200 W, for example.

</ol>