Calculating the Ionic strength of sodium acetylsalicylate
Aspirin has a solubility of ~3 g/L. In addition from a patent by Galat [1]:


  Sodium aspirin is almost 1000 times as soluble in water as aspirin itself.


All of the $\ce{NaOH}$  can be assumed to react with acetylsalicylic acid (aspirin) to form the sodium salt.  This means the amount of solubilized sodium aspirin is roughly equal to the amount of added $\ce{NaOH}$ (up to the equivalence point). 

When computing the ionic strength you can therefore assume that the concentration of solubilized sodium aspirin is roughly equal to the amount of added $\ce{NaOH}$.

References


Galat, A. Stable Sodium Acetylsalicylate and Method for Its Manufacture. US3985792A, October 12, 1976. (PDF)