You can check for collinearity for logistic regression the same way as you would for linear regression i.e. just run a linear regression with the same predictors and dependant you are using for the logistic model. You are just running it to get the collinearity stats and then interpret these the same way.

Others may be able to comment more on this, but some suggestions for solving it (each with their own issues); is remove one of the colinear measures (obviously not ideal!), just leave it in and comment on it in your report as an issue, or you could factor analyse the collinear measures to get a factor score for them and use the factor score.

Hope this helps