One can obtain odds ratios from the results of logistic regression model. Odds ratios derived are adjusted for predictors included in the model and explains the relationship between two groups (e.g., treatment and control group) and outcome (binary outcome). I wrote the following Excel document that calculates odds ratio based on logit coefficients from the intercept and the predictor of interest (binary ones: e.g., impact coefficient, gender effect, etc.).
Appendix (p.27) of the following document includes description of odds ratio.