After I turn off my car I hear a loud humming sound like a motor running from a part under the hood on the right side and a black tube that goes to it is vibrating.humming sound. What is it?

If the engine is not reaching optimum operating temperature it will indeed give you a "check engine light",the code will lean you in that direction as well.The noise your hearing more than likely is coming from the "clutch fan",they are very common on the TrailBlazers to make noise and fail.The oil light... you certainly need to have the oil pressure checked with a mechanical gage.

cvc joints

It probably is your radiator cooling fan. It will run until the car temperature drops to near level temperature The line vibrating is more than likely just vibration of the which is nothing unusual.Hope this helps;
Gikkight

the noise is coming from the wheel section, it's called air splash, humming varies with speed, main causes are wheel alignment due to loose ball joint, check if your tire erodes on one side, next check your disc brake for clogged air cooled vain and disc wearing

It could be the ABS. MY HONDA DOES THE SAME THING.
I took it to PepBoys yesterday and they could not connect to the
computer interface.They said I need to take it to a honda dealer
so they can connect and determine what is wrong with the
Automatic breaking system. The noise is the ABS motor
turning on and off.

sounds like the transmission solenoids in the trans. Does your speedo work ok?

go here for villager help

http://autos.groups.yahoo.com/group/villagerquest/

The black box is under the hood right in front of the battery. Once you release the 2 plastic clips on either side, it will lift off. The ufel pump relay should be identified on the chart inside the cover. I believe it is green. It just pulls out.
Question. If you listen carefully when you turn the key on, can you hear the fuel pump hum for about 2 seconds? It is in the fuel tank, so listen back there whil someone turns the key on. Also, the pump should run all the time while the engine is cranking. It only runs for 2 seconds when you turn the key on if the engine is not running. (safety thing).

Sounds like you need a fuel pump. The first indication of a fuel pump issue is a hum or drone noise.

There is an ABS fuse under the hood that you can take out, and the noise will quit. The noise is accually your ABS pump. They are kind of expensive.