Cannot execute statement: impossible to write to binary log?
It looks as if your server is misconfigured, or (though somewhat less likely) your code is improperly setting the binlog_format system variable for the current session to STATEMENT (apparently these incorrect modes of operation are, appropriately, more aggressively prevented in 5.6, so I assume you are using something earlier).

# In order for Galera to work correctly binlog format should be ROW
— http://www.percona.com/doc/percona-xtradb-cluster/5.5/manual/bootstrap.html
any binlog_format other than ROW was never supported (also well documented)
— https://bugs.launchpad.net/percona-xtradb-cluster/+bug/1263991

This should be the configuration in all of your nodes in my.cnf.  If your cluster has been running without this, the nodes may not be consistent, though it's hard to imagine it running like this at all, though there were cirumstances in older releases that allowed the server to start with invalid configuration when it should not have done so.