You can calculate the relative risk of having the disease given exposure in R, by using a The odds ratio is also commonly calculated in a case-control study.
The coefficient returned by a logistic regression in r is a logit, or the log of the odds. To convert logits to odds ratio, you can exponentiate it, as you've.
Producing odds ratio output seems to require installing epicalc and/or . regression in R. It includes a brief section on calculating odds ratios.