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I have a shapefile in which I need the symbology to be both size graduated and to represent another variable (say for example, "yes" or "no"), and another variable that is a numeric amount (say, from 1 to 10).
I'm attaching a diagram to illustrate what I want.
I would try using an SQL selection to get features for each text variable and then make an individual layer for each. Those can be styled according to the ordinal value, in your example, red for the "no" layer/blue for the "yes" layer etc.
For the symbol size, you can use the same variable and scale across all of the layers, but they'll stay different colors.
If the attributes are stored as two fields, have you tried to use the "Unique values, many fields" within the Layer properties symbology tab under Categories? You could select the two symbology-defining fields and add the values. This method would require manually setting the symbology style (ie in your example of two string options and ten numerical options it would produce up to 20 individual styles).
