Can I take a oxycodone and naproxen at the same time?

Yes really that is a pretty common combination. But just remember if the stomach gets upset to take them With food if you have not had them before.

Yes you can since they are 2 different types of pain relievers. It may be beneficial also. Oxycodone is an opioid and Naproxen is an NSAID (non steroidal anti inflammatory drug). An opioid just helps with pain, but naproxen helps with pain and swelling.
I am prescribed both of these medications by my pain doctor and take them together often.