Crude rate is number of cases over population at risk. One must be careful to define numerator and demominator of any rate. Specific rate is the rate for s sub-population. Eg age standardized rate assumes particular age distribution. It is a measure of incidence.
Relative risk is a ratio formed from comparison of two levels of risk.
The Odds ratio is a ratio comparable to relative risk except that it is formed from two sets of odds. Odds differ from risk rates in that the positive cases in the numerator are not included in the denominator. This formulation has useful statistical properties when presented as logarithms. Odds ratios and relative risk statistics become equivalent at very low incidence or prevalence rates.