To evaluate the expressions at the specified variable values, we'll substitute the given values of \(x\) and \(y\) into each expression.

### e)
\[
E = -x(x - y)^2 + (x - y) + y(y - 2x)
\]
**Substitutions:** \( |2x - 1| = 1 \) implies \( 2x = 2 \) or \( 2x = 0 \) (so \( x = 1 \) or \( x = 0 \)), and \( y = -2 \). We take \( x = 1 \) (since \( x = 0\) will yield \( E = -1 \)).

\[
E = -1(1 - (-2))^2 + (1 - (-2)) + (-2)((-2) - 2 \cdot 1)
\]
Calculating each term:
\[
E = -1(3)^2 + 3 - 2(-4)
= -9 + 3 + 8
= 2
\]

### f)
\[
F = -(2x - y) - x(2x - y) - y
\]
**Substitutions:** \( x - 2 = 0\) implies \( x = 2 \) and \( y^2 = 0\) implies \( y = 0 \).

\[
F = - (2 \cdot 2 - 0) - 2(2 \cdot 2 - 0) - 0
= -4 - 8
= -12
\]

### g)
\[
G = (x + y)(x^2 - xy + y^2) + 3(2x - y)(4x^2 + 2xy + y^2)
\]
**Substitutions:** \( x + y = 2 \) and \( y = -3 \) implies \( x = 5 \).

\[
G = (5 - 3)(5^2 - 5 \cdot (-3) + (-3)^2) + 3(2 \cdot 5 + 3)(4(5^2) + 2(5)(-3) + (-3)^2)
\]
Calculating each term:
\[
= 2(25 + 15 + 9) + 3(10 + 3)(100 - 30 + 9)
= 2(49) + 3(13)(79)
= 98 + 3081
= 3179
\]

### h)
\[
H = (x + 3y)(x^2 - 3xy + 9y^2) + (3x - y)(9x^2 + 3xy + y^2)
\]
**Substitutions:** \( 3x - y = 5 \) implies \( y = 3x - 5 \) and \( x = 2 \).

Substituting \( x = 2 \):
\[
y = 3(2) - 5 = 6 - 5 = 1
\]
Now substituting \( x = 2 \) and \( y = 1 \):
\[
H = (2 + 3)(2^2 - 3(2)(1) + 9(1)^2) + (3(2) - 1)(9(2)^2 + 3(2)(1) + (1)^2)
\]
Calculating each term:
\[
H = (5)(4 - 6 + 9) + (6 - 1)(36 + 6 + 1)
= 5(7) + (5)(43)
= 35 + 215
= 250
\]

### Summary of Results:
- \( E = 2 \)
- \( F = -12 \)
- \( G = 3179 \)
- \( H = 250 \)