Logistic regression odds ratios comparison?

If I have a logistic regression model with several independent variables that are all significant at the .05 level, what can I say about their contribution to the model? I have understood that odds ratios are effect size measurements but I'm uncertain of how to interpret them as such. Do larger odds ratios indicate a greater effect on the dependent variable? Can you compare the odds ratios between different independent variables? For example, if I have two categorical variables, education and gender, and the odds ratios for the education categories vary between 1.5 and 3 (for example education level 2 has an odds ratio of 1.5 with the reference group, level 3 has an odds ratio of 2, level 4 an odds ratio of 3), and the odds ratios for the gender groups vary between 5-7, are the larger odds ratios for gender any indication that gender would be a 'stronger' predictor in the model? Thanks in advance!