I would start with estimating a (simple) bivariate correlation matrix which includes your outcome variable as well as all predictors. This will give you very first insights into the dependency structure of all your variables. Especially correlation coefficients of $|r| > 0.4$ (between your predictor variables) can indicate later multicollinearity problems.
Next, I would continue with a series of bivariate regressions. That is, for each predictor ('independent variable') run one logistic regression. One of these regressions will focus on your control-/treatment-group variable. This will inform you about the 'gross' effects, that is the unadjusted effects. Please, do not think that statistically non-significant effects could be excluded from later analysis.
Do you assume an interaction effect between HIV and your treatment-variable (1=treatment, 0=control)? Then you could run two separate models with HIV as predictor variable, i.e. one model for control- and one model for treatment-group. Given that you observe different coefficients for HIV, you will need to run another model which includes an interaction effect $HIV \times treatment$ (and the two main effects). This second model will allow you to test for statistically significant differences between the groups. You also might include your other predictor variables.
Please be aware that interaction effects in logistic regression models are more complicated than in the case of a simple linear regression model. Edward Norton has published several papers which discuss that topic.
You also did not tell us what software you are using to estimate the models. However, most software packages are able to test for multicollinearity (VIF or tolerance).