Throw it in the recycling skip at your local council tip and buy a proper system
Bit drastic maybe but you have discovered one of many reasons why I will never ever recommend anyone buys an all in one system like this. They are next to useless if you have anything more than than just a TV to plug into it.
The surround system does have ARC so if the TV also has an ARC wired HDMI socket you can use that to get audio back from the TV if you use the TV's built in Freeview. That leaves the optical in free for the TiVo or the PS4 but you will need an external optical switch if you want to avoid lots of re-plugging.
Depending on the capabilities of the TV it should be possible to connect the TiVo and PS4 via HDMI to the TV and either use the ARC on the surround or the optical connection to get audio from both of those back to the surround system.
This will give you at the very least stereo audio from the TiVo and PS4. Possibly with Dolby ProLogic encoded surround information, depending on the capabilities of those devices. The TV may be able to pass Dolby Digital surround from the HDMI inputs to the optical/ARC output. But that is not guaranteed, might have to suck it and see.