Statistics: Which test to use to find the relation between two binary variables adjusted for a continuous and two binary covariates? How do I check for covariates in the first place?

Still trying to figure stats, bear with me
OK. My data
1) My outcome variable (Outvar) is binary (yes/no)
2) My explanatory variable (exvar) is also binary (yes/no)
3) I have 3 variables:
Variable A is binary
Variable B is continuous but not normally distributed
Variable C is also continuous and has normal distribution
For the varA, varB and varC, I want to check if they impact my outcome variable. If they do I want to “remove” their impact because I want to know the independent impact of my exvar on outvar. Which test should I use?
And, do I need to check the impact of varA, varB, var C on my exvar too?

this may be easy but I am so unable to think right now
if it is of any importance I am using the SPSS v20 for creating all these statistic questions in my head