Your problem is not with ssh, but rather in DNS resolution. If you will add
192.168.1.162 oel5.server2.com server2
to server1's /etc/hosts file AND
192.168.1.160 oel5.server1.com server1 to
to server2's /etc/hosts file, then each server will know about the other. Currently, you have no way to resovle the other severs IP by name on either server.
To ensure the issue is not with shh, try ssh using IP rather than name:
if this fails, try the above sith ssh -v and post the results