Here is what each of those probably does. I am not 100% sure though b/c different models call things different names. Remember that almost all night shots benefit from using a tripod and using a wide angle instead of telephoto. Using a 2 second delay from pressing the shutter to the actual shot helps keep your finger motion from messing up the shot. Most cameras have that feature, but it may only allow something like 10 seconds.
portrait - It has a slower shutter, but proably not enough for night shots
fireworks - It should set the shutter to around 2 secs. a small aperture (~f/8)and a low ISO. It might vary from that.
night - this is probably for night portraits. If it includes a flash, then that is probably right. If so, it has a long shutter speed (at least a second) to capture the background and a flash to capture your subject.
night landscape - this should be a long shutter speed and no flash
backlight - This should be for daytime shots when there is light behind your subject. To properly capture the subject without overexposing everything else, it uses a flash.
To do a manual night portrait, have the camera set for a proper exposure of the background and then tell the camera to use a flash. Do not have the flash turned on while it is metering for a proper exposure of the background. You might want to try testing the settings it gives you in P or Auto mode and then enter that in manual mode and include the flash. You want to focus on the people.
To do a night shot of something not moving, then you can probably just let the camera decide what to do as long as you use a tripod.
To do a night shot of a moving subject without flash, then you have to sacrifice. You either have to increase the ISO, which means more image noise, or use a wide aperture (~f/2.8-3.5 on a p&s), which means less depth of field. You will likely have to do both. You must maintain a fast enough shutter speed to keep the motion from blurring the shot. You might not need a tripod though b/c of the faster shutter.
Kevin