Any of these three measures are valid comparisons of the probability of disease between two groups. (I say three because relative risk and risk ratio are the same thing.)
For case-control studies, you can only use the odds ratio because you do not have a valid estimate of risk. In case-control studies you choose the number of cases and number of controls, so you cannot provide an estimate of risk.
Risk ratios can be misleading as to the importance of the difference when the risk in the comparison group is very small. For example, if the risk in the unexposed group is 0.01 and the risk in the exposed group is 0.05, that leads to a risk ratio of 5, but a risk difference of only 0.04. On the other hand, if the risk in the unexposed group is 0.05, but the risk in the exposed group is 0.25, you still have a risk ratio of 5. But the risk difference is now 0.2! Therefore, the importance of risk ratios depends upon the baseline risk for the disease in the unexposed group.