How do I get audio out for headphones when there is no audio out from projector or home cinema player?

https://community.sony.co.uk/t5/home-cinema-projectors-players/how-to-repair-sony-hcd-zux10d-dvd-deck-receiver-always-display/td-p/2295791

Trying to understand your problem. Sounds like an orientation problem with your projector. Check your manual to get image orientation setup correctly for your projector. Look for projecting image onto the front of screen instead of projecting image thru the back of screen. Some times the application calls for projecting from behind screen just like a projection TV.

To me itcsounds like ypu have a 1080p signal, 1080i is what it accepts. The 1080p signal will only show up on half the screen. Switch blue ray player to 720p or 1080i output.

Generally speaking, if your Home Cinema system is able to pass-thru video as well as audio, you'll want to take the HDMI cable from the XBOX video out, into the Home Cinema system's input (any HDMI input should be fine), and then run the HDMI video out to your projector. Any other devices you want to be able to project as well (DVD/BluRay, PC, Cable, Satellite, etc.) would also be plugged into the Home Cinema system as "in" devices, like the XBOX.

When you want to display one of those devices, you would select that "in" port's input name in the Home Cinema system (for example, if the XBOX is connected to the HDMI in that is labeled "aux", you will switch the cinema system to Aux Input, and the projector should immediately begin getting the signal from the theatre system. To switch to another device, you simply change the Input channel on the Home Cinema.

The audio also, providing the device (the XBOX) can carry it on the HDMI cable, will also be delivered to the Home Cinema. Some devices cannot carry sound on HDMI (though many can). For those, you will need to run an HDMI cable for the video, and also an optical cable or other type of audio-only cable, for its audio. You do not need to run an audio cable to the projector though, as the projector is only for video. The Home Cinema will take care of the sound itself.

connect an audio lead from the headphone socket on your laptop to a audio input on the home cinema

Yes, you will need a DVD player and a sound system, you can connect an HDMI cable from your DVD to the Optoma and then a digital audio cable from your DVD player to your sound system.

I bought the optical audio cable ($15 WalMart) and use the Digital In on the DVD player to play the sound through the surround system and turned the TV speakers off. Works great! The optial audio has square ends and looks transparent with just one round shaped cable that goes from the TV to the back of the DVD player.

PUT A SET OF PHONO CABLES FROM AUDIO OUT ON SKY TO AUX INPUT ON YOUR SAMSUNG.SWITCH SYSTEM TO AUX INPUT SET SOUND 2 PROLOGIC 2,AND HEYPRESTO SURROUND SOUND I HOPE.

HOPE THIS HELPS.
CABLE GUY.