What am I doing wrong?

Using Arduino Programming Questions
1

I am trying to use analog potentiometer inputs and convert them to digital outputs. I read that the digital outputs are in-between the values 0 and 1023, so I wrote the following code:

//reads analog and converts to digital
//then it uses the digital output to turn on LEDs

int red = 7;
int green = 8;
int yellow = 9;
int val = 0;

void setup() {
pinMode(red, OUTPUT);
pinMode(green, OUTPUT);
pinMode(yellow, OUTPUT);
Serial.begin(9600);
}

void loop() {
val = analogRead(A2);
Serial.println(val);
delay(1);
if (val >= 0 || val <= 255)
{
digitalWrite(red, HIGH);
}
else if(val >= 256 || val <= 511)
{
digitalWrite(yellow, HIGH);
}
else if(val >= 512 || val <=1023)
{
digitalWrite(green, HIGH);
}
}

There are no compiling errors.
The problem is only the red LED turns on and stays on. When I turn the potentiometer nothing else happens.
I am using an Elektor R4 board.
My TX LED is always on and my computer is connected to the board
I am also new to Arduino so please go easy on me. Am I doing something wrong, and is there an easier way to accomplish this?

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2 
if (val >= 0 || val  <= 255)

Any value of val read from the pot will be greater than 0.

I suspect you meant

if (val >= 0 && val  <= 255)  //and instead of or in the comparison

in order to act on a value between 0 and 255 and so on for other ranges.

3

Thank you, I will try this when I get back from school.

4

There's also no code to turn any of those leds off, so once they're on they're on for good.

5

Yes everything works perfectly, forgot about turning off the LEDs too, thank you for that.