The jack on the Xbox 360 controller is a 2.5mm combination mic/mono speaker jack. I haven't tested this myself, but I've read that the pinout on the headset connector is mic/speaker/ground going from the tip towards the cable.
Microsoft doesn't really publicly specify the characteristics of mics that can be plugged into this port. No doubt there are some specs, so I can't say for sure that any generic mic plugged properly into this port would work.
When a headset is plugged into this jack, the game audio continues to be routed to the A/V connectors (ie, Component, HDMI, and/or optical) on the rear of the unit, but any voice chat audio is routed to the mono speaker jack on the controller. Without a headset, all of this audio is routed to the A/V connectors on the rear. Therefore, you can't plug a headset into the jack on the controller and turn the TV volume all the way down and expect to hear the game audio. Likewise, I don't believe you can plug in a mic and not a mono speaker to this jack without killing voice chat audio.
You can try to somehow mux the TV's (or your receiver's) audio into the voice chat audio in some fashion, but that can be a challenging DIY project. Just plugging it all together might work, but controlling relative volumes and signal issues/current flows might get awkward or complicated without at least a rudimentary knowledge of audio electronics hardware.
There are also third party headsets that handle this connection for you, and I've heard mixed reviews of such devices, so make sure you look into reviews of any specific models before you make a purchase.
What I personally use is an Astro Mixamp which is a wireless device that connects to the TV (optical), the controller, and a standard PC headset, and properly routes the audio around the room. You say you've already got a good Sennheiser headphone set - this is exactly the setup I use at home, a PC151 hooked to the Mixamp and my controller/the TV.
Best Answer
For the PlayStation 4, you can just use a regular set of 3.5mm headphones to hear game audio through the port on the DualShock 4.
To do so, from the PS menu, go to Settings > Devices > Audio Devices > output to Headphones > With your headphones plugged in select "All Audio" as opposed to "Chat Audio." You can also adjust the volume from Audio Devices > Volume Control (Headphones).