<p>I have an Java desktop application which connects directly with the DB (an Oracle). The application has multiple user accounts. What is the correct method to send the user's password (not DB password) over the network? I don't want to send it in plain text.</p>

If you don't want to send the data in plain text, use encryption !!!
Use some encryption algorithm such as AES, Twofish etc.
You must also take into consideration where your client and server are. If they both are in the same machine, there is no use of using an encryption. If they are in different machines, use some encryption algorithm to send sensitive data.
If YOU are checking the validity of the passwords, you can just send the hash of the password. Beware that this method will work only if you are comparing the password yourself. If some other application (out of your control) is doing the validation job, you cannot hash the password.