To understand the significance of using this transformer in the way you want, we need to look at how an autotransformer is designed. But first let's recap what you know about this one.
The primary is almost certainly intended for two options of supply voltage that would typically be selected by a concealed switch on the equipment. The high voltage option would use the ends of the winding, black and yellow, The lower voltage would use black and the blue tap. Most of the primary turns are between black and blue, with a smaller number between blue and yellow. The turns ratio is in proportion to the voltage ratio: If 200V on blue gives 250V on yellow, then the blue tap is at 4/5 of the total number of turns. This is an unusual position for the tap, I would expect to see nearer 220/240 for typical supply voltage options. There is a possible alternative explanation for the function of the tap but it's not important to go into that here.
Regarding the resistance measurements; obviously the resistance between the ends of a winding is the sum of all the resistances from each end or tap to the next. Resistance measurements are useful to find the order of the taps and identify their likely functions, but will not tell you the voltage ratios accurately because not all turns have the same length of wire. If the black end is near the middle of the winding each turn between black and blue will be shorter than between blue and yellow so the resistance ratio will be different to the turns ratio that governs the voltages.
It is not normal to mark the wire gauge on a transformer. If you are reading the 18AWG off the lead-out wire, it only relates to the lead-out itself, not to the transformer winding and tells you nothing about the transformer's rating. The best way to assess the VA rating is to compare the size and weight to transformers of similar design and function. There are limits to which the iron and copper can be worked, and in all commercial power transformers these are adhered to quite closely. Therefore the weight of material is closely linked to the VA rating. I mention comparing similar designs because special types of transformer with extreme voltage or currents, or transformers other than normal AC power types, might not have comparable size and weight.
What you want to do is to operate the primary as an autotransformer (input and output on the same winding) with the input on the blue tap and output at the yellow end of the winding, to increase the voltage by the turns ratio. You are probably aware of the basic relationships with any transformer: Power out = power in. Vout / Vin = Iin / Iout, ignoring losses. You want to step up with Vout = 5/4 x Vin and therefore Iin = 5/4 Iout, and discover what load the transformer can safely handle.
I will spoil the plot here and say that for this ratio, the safe load is in the same ballpark as the transformer's official VA rating, so if you have a transformer comparable in size to a commercial 100VA transformer, you could connect 100VA load to it. But the reason for this is more a coincidence than because of any relationship between the VA rating and the load. It would not apply if the voltage ratio were over 1:2; you might be limited to a lower load VA than the transformer rating. It's interesting to explore the reason behind this in an autotransformer.
If you were drawing the output from a secondary winding you would need a transformer equal in VA rating to the load. The primary would be wound for Vin and Iin, and the secondary for Vout and Iout. The winding wire size will be matched to the current. In the case of a step-up the primary will be wound with larger wire because Iin > Iout. If the voltage (and hence current) ratio is large, the wires will be very different sizes.
In an autotransformer, different currents flow through different parts of the winding. In your step-up application, the current through the blue lead will be Iin, that through the yellow Iout, and that through the black the difference between the two. Now we come to the important bit. In your auto connection, only the 1/5 extra voltage and hence 1/5 of the load VA is being transformed. The other 4/5 comes directly from the supply. So for an auto stepping up 4:5 the transformer only needs to be a fraction of the size of a comparable double-wound transformer. This is why auto configuration is much more economical when only a small voltage ratio is needed. But your transformer will not handle a load of 5x its VA rating because the wire of the section of winding carrying Iout is only of a size rated for rated VA at Vin. In a purpose-made autotransformer, that part of the winding would be rated 5x higher. Your transformer will however in theory handle a load slightly greater than its VA rating, because there is no heat dissipation from the unused secondary and the current in the main 200V part of the primary is much lower than designed (only Iin-Iout) so the heat dissipation in the 50V part could be allowed to increase a little. Therefore Iout could be higher than the designed Iin.
The take-away from this is that when a double-wound transformer is re-purposed as an autotransformer, the limiting factor might be the winding current rating, not the overall VA rating. But you can make your own autotransformer that does use all its VA capability. A boosting or bucking connection takes a double-wound transformer with a low-voltage secondary and connects that in series with the primary. Now you have the necessary difference in wire gauge to allow for the full Iout and in your case a transformer with a 50V secondary stacked on top of the primary will power a load VA of Isec x Vout or around 5x the transformer VA rating.
But note the point made by
@Rockingit: If your mains supply goes up to 'normal' volts the output will be very high and might damage your equipment. This needs serious consideration.
