Why bucketing of continuous variables is preferred in logistic regression ? What is the funda behind adjusted log odds ratio and unadjusted log odds ratio when we have a continuous variable ?
Bucketing (making groups) of continuous data usually ought not be favored for independent variables in logistic regression, any more than it is in linear regression. Unless there is strong theory behind the groups, it will lose information. It is better to use polynomial terms of spline terms to account for any non-linearity. Douglas Altman has written about this in several places e.g. Encyclopedia of Biostatistics.
It is done a lot because 1) It is "easier" than learning about polynomials and splines and 2) Because "that's what other people do".
The odds ratio for a continuous variable is the odds ratio per unit of that variable. E.g. if you are predicting whether a person votes Republican or Democrat and one of your IV is "income in thousands of
$ per year" then the OR is the change in the odds per $1,000.