If your monitor happens to have speakers built in then you can use a 1/8" (3.5mm) male stereo jack to female stereo RCA jack cable or adapter to connect your PlayStation 3's RCA cables to your computer monitor.
Assuming though that your monitor doesn't have speakers, but you do have a PC near your computer monitor there is a way you can hear your PS3's audio on your USB headphones by connecting your PS3 to your PC. This also requires a 1/8" (3.5mm) male stereo jack to female stereo RCA jack cable or adapter.
First connect the composite AV cable that came with your PS3 to it's AV MULTI OUT port. Then connect the red and white male RCA connectors of the AV cable to the female RCA jacks of the previously mentioned cable/adapter. Then plug in that cable/adapter to the line in jack at the back of your PC. This jack should be coloured light blue. You might get some sort of pop-up on your PC when you do this, you many need acknowledge that you've plugged something into the line in connector.
Now go into your PS3's settings menu and change the audio output device to AV MULTI: Seettings -> Sound Settings -> Audio Output Settings -> Audio Input Connector / SCART / AV MULTI. If possible start playing a game or MP3s on your PS3 so it's outputting audio continuously during the remainder of these steps.
Plug your USB headphones into your PC and right click on the speaker icon in the task bar notification area. (The rest of these instructions assume Windows 7, but there should be a similar way of doing this on Windows 8 or later.) Select "Recording Devices" on the menu and look for a "Line In" or other similarly named device. If your PS3 is currently outputting audio you should see a graph next to it showing that device is receiving audio. Select it and press the "Properties" button.
Now select the "Listen" tab of the line in device's property window. Click the "Listen to this device" check box and select your USB headphones from the drop down box below it. Then press the "OK" button and you should be able to hear your PS3's audio on your headphones.
Note you might need to play around with the volume and recording levels. Keep your headphones off your head when you first do this in case the volume is too loud. If you can't hear anything with the headphones on you may need to turn up the levels.