A). To change Mysql innodb_log file to a new location.
1. Change my.cnf settings for innodb_log file or innodb_fast_shutdown=0
(so it does full flush of log files from buffer).
2. Stop mysql.
3. Change innodb_log_group_home_dir = /mysql/new_location/ in my.cnf.
4. Start Mysql, it should be up now.
B). To change Mysql log_error file to a new location.
1. Create a new file for log_error file OS level.
- copy nul > /mysql/NEW_LOCATION/mysql_error
- Give mysql permission to /mysql/NEW_LOCATION/mysql_error to read and write.
2. Change my.cnf log_error = /mysql/NEW_LOCATION/mysql_error
3. Stop Mysql.
4. Start Mysql.
You may do A and B in one shot, I will let you do organize which ever way you wanted.