Hi,
just logon to the Oracle server and observe
netstat -an
ourput if you can see port 1521 is listening then it seems that Oracle Listener is active. So this must not be a db issue. If not start oracle listener.
Try to telnet as ajay-singh suggested over the Oracle system. If you succeed then try to telnet to the same system over the websphere server. If you can not succeed then it must be a firewall or routing problem and most likey that the firewall over oracle server or a firewall in between..
Will you please elaborate about your local setup? Are both systems (websphere, oracle) located on the same subnet? Are there any gateways in between? Any firewalls ? Can you ping to the Oracle system from Websphere system? Vice versa?
Cheers,
K.