odds and expected B

#1
am doing a cross sectional study, now analysing my data. since my data (the outcome is yes and no) and the independant variables all are catigorical (either from the start or i concert them as age --> age catigories), i used chi square to test the association.
but my litherture show some studies using also odds ratio and CI in their tables.

i tried first to calculate odds for variables when three is two catigories . i.e. when 2x2 contagious table with my out come possible using spss analyse cross tab --> risk
this was ok, but for those variables with more than two catigories it is not possible.

i go to binary log. regression , where i can calculate the expected B , which if i am not wrong is the odds ratio, or the odds of the outcome for each catigory of a given variable , using one catigory as referance

first i would like to know if i am right in doing that
and then,
i noted that , for those variables with two catigories which i got the odds ratio from the risk order in the cross tab in spss , that odds not the same number of the expected B

is it ok if i just fix on reporting the odds using the expect B ??