If these are the only traits in which you're interested, then you can either correlate the module values to these (with the traits encoded numerically as 1, 2, 3, etc), or, better, build a multinomial logistic regression model with the module values as x and time/strain as y ( glm(time/strain ~ Module1); glm(time/strain ~ Module2); et cetera)
You may also have to consider dividing up the analysis into multiple analyses, and contrast/compare the results manually. For example, running WGCNA separately for the different time-points may be an idea, and then building the regression model predicting for virus strain each time.
That decision is for you to make.
I will wait for response of people with similar experience