Is it safe to say that Logistic regression using maximum likelihood will produce highly bias odds ratios? If so, what other options do I have? I came across Penalized Likelihood /Firth method, as well as Exact Logistic regression, but NONE of those are available on SPSS.

Do you think my best bet is just a Chi Square to estimate the contingencies between the DV and the IV's, and forget about my dreams of modelling their likelihoods?