The models in EnergyPlus are generally too complicated to write analytic expressions for sensitivity. You thus really have to do this numerically and that involves lots of runs of EnergyPlus. To do that you should use one of the software packages for doing parametric studies like JEplus. Maybe someone who has used JEplus can share some scripts for doing sensitivity analysis.
You have three main options
1) Local sensitivity analysis of individual variables where you would do small variations on the value of an individual parameter and then compute the sensitivity using numeric approximations to the derivative. This is also called one-at-a-time sensitivity analysis. This is a poor approximation when you have nonlinear models with a large parameter space like you do in buildings.
2) Global sensitivity analysis where you select the parameters to study and then use a sampling method like Latin Hypercube Sampling to explore the parameter space with a limited number of runs and then use variance analysis to estimate the sensitivity. This is, in my opinion, the best solution but takes the most computing time
3) Pseudo global sensitivity analysis methods like the Morris method. These are also one-at-a time methods but they try to analyze more of the parameter space than standard one-at-a-time methods. The resulting values are not true sensitivities but are useful for ranking the importance of variables.