Q:

What am I missing in this python? It's a simple program to order 3 terms, and the last order part doesn't work

I already tried inputting the SWAP() function directly, and it works, but with the function inside it doesn't swap the variables.
def SWAP(x,y):
    w = x
    x = y
    y = w
    del w

def ORDER(x,y,z):
    if x > z:
        SWAP(x,z)
    if x > y:
        SWAP(x,y)
    if y > z:
        SWAP(y,z)
    print(f'{x}<{y}<{z}')

A:

When you are calling SWAPfunction it is not returning the values. And function args are not sent as call-by-reference.
So what ever changes you do in SWAP function does not get reflected in the calling function.
Try this :
def SWAP(x,y):
    w = x
    x = y
    y = w
    return x,y

def ORDER(x,y,z):
    if x > z:
        x,z=SWAP(x,z)
    if x > y:
        x,y=SWAP(x,y)
    if y > z:
        y,z=SWAP(y,z)
    print(f'{x}<{y}<{z}')

Explanation :
SWAP function takes 2 args x,y and returns the swapped value. Swapping done by you was correct.
While calling SWAP I am expecting a return of 2 variable which should be swapped. 
Eg. - 
a = 5
b = 8

a,b = SWAP(a,b)

Here I am calling SWAP with `a,b` who have values `5,8` currently, 
Now SWAP returns `8,5`as response. I am storing `8,5` into `a,b`. 

So Now a becomes 8 and b becomes 5. 

All the other logic is same as you wrote for comparing.

