The coefficients most certainly have a meaning. In some software packages the model can be directed in either of two ways to produce either of two types of coefficients. For example, in Stata, one can use either the Logistic command or the logit command; in using one, the model gives traditional coefficients, while in using the other, the model gives odds ratios.
You may find that one is much more meaningful to you than the other.
About your question that "...coefficients seem to depend sensitivity...".
Are you saying that the results depend on what variables you put in the model?
If so, yes, this is a fact of life when doing regression analysis. The reason for this is that regression analysis is looking at a bunch of numbers and crunching them in an automated way.
The results depend on how the variables are related to each other and on what variables are not measured. It is as much an art as it is a science.
Furthermore, if the model has too many predictors compared to the sample size, the signs can flip around in a crazy way - I think of this is saying that the model is using variables that have a small effect to "adjust" its estimates of those that have a big effect (like a small volume knob to make small calibrations). When this happens, I tend to not trust the variables with small effects.
On the other hand, it may be that signs initially change, when you add new predictors, because you are getting closer to the causal truth.
For example, lets imagine that Greenland Brandy might be bad for one's health but income is good for one's health. If income is omitted, and more rich people drink Brandy, then the model may "pick up" the omitted income influence and "say" that the alcohol is good for your health.
Have no doubt about it, it is a fact of life that coefficients depend on the other variables that are included. To learn more, look into "omitted variable bias" and "spurious relationship". If you have not encountered these ideas before, try to find introduction to statistics courses that meet your needs - this can make a huge difference in doing the models.