This consider all database names are different on all server.
As you said all servers are mysql 5.1, You can take mysqldump on each server and restore it on new server
Step 1 : Take dump from all old server like below
Everything written in one file: table structures, indexes, triggers, stored procedures, users, encrypted passwords.
mysqldump -u... -p... --routines --triggers --all-databases | gzip > MySQLDataServer1.sql.gz
mysqldump -u... -p... --routines --triggers --all-databases | gzip > MySQLDataServer2.sql.gz
mysqldump -u... -p... --routines --triggers --all-databases | gzip > MySQLDataServer3.sql.gz
mysqldump -u... -p... --routines --triggers --all-databases | gzip > MySQLDataServer4.sql.gz
Step 2 : Copy dump from all old servers to new server
Step 3 : Extract all zips on new server
Step 4 : Import extracted dump files on new server like below
mysql -u... -p... < MySQLDataServer1.sql
mysql -u... -p... < MySQLDataServer2.sql
mysql -u... -p... < MySQLDataServer3.sql
mysql -u... -p... < MySQLDataServer4.sql
MySQL Versionis same on all older as well as on new servers ? – Abdul Manaf Feb 26 '14 at 09:21