How can I play music online using my PSP without any softwares installed in it or without a memory card?

I do not have a memory card and I want to play videos or music online> I just bought by PSP… with a 3.80 firmware installed and with flash but it dosent play videos and it can just play online games..

Without a memory stick you will be abe to save anything. Which means you won't be able to play MP3's or MP4's.

I believe with 3.80 you should have the Internet Radio Player installed. You can find it above the Internet Browser from the XMB. This radio is basically a streaming audio player that uses the Flash Player in the web browser.

As far as watching Video from the Browser, you can't. You can get some flash animations and games http://www.psponme.com. But you are either going to need WiFi from your PSP or a memory stick to save them from your PC to your PSP.

There are some homebrew video players for things like Youtube, it does not use the PSP browser and you will need to have a memory stick to use it.