Turns out, a lot of this equipment was taken from other ships of the era. So this wasn't necessarily what was installed on the Intrepid at the time of its decommission, but would have likely been found here at some point (like the radar display in the foreground).
Here you can see a few more of the plane/helicopters I didn't have the room to have full images of, like the Harrier (which I featured in my RAF Museum Tour). Going left to right from there, a Huey, Sea Cobra, Chickasaw, Seaguard, Kfir, and the others I showed earlier.
Just below frame is the wheel used to steer the ship, using one of these redundant compasses. The tubes are backup for backups, but ensure communication to other important areas of the ship even if power is lost.
While the lease on the Intrepid is only $1 a year, the museum still has to maintain it. Many off-limits areas are probably that way because of cost to make them publicly accessible/safe. That yellow warning sign, for instances, says "Asbestos."