Let's break this down step by step.

First, we need to convert all the mixed numbers to improper fractions.

5 4/9 = (95 + 4)/9 = 49/9
7 5/6 = (67 + 5)/6 = 47/6
4 5/18 = (18*4 + 5)/18 = 77/18

Next, we need to find the absolute value of -7 11/27.

-7 11/27 = -(27*7 + 11)/27 = -200/27

Now we can plug everything back into the original expression:

49/9 - 47/6 + 77/18 - |-200/27|

To simplify further, we can find the absolute value of -200/27:

|-200/27| = 200/27

Now, the expression becomes:

49/9 - 47/6 + 77/18 - 200/27

To add and subtract these fractions, we need to find a common denominator. The least common multiple of 9, 6, 18, and 27 is 54.

Converting all the fractions to have a denominator of 54:

49/9 = 245/54
47/6 = 282/54
77/18 = 154/54
200/27 = 400/54

Now the expression becomes:

245/54 - 282/54 + 154/54 - 400/54

Adding and subtracting these fractions:

245 - 282 + 154 - 400 = -283

Therefore, the final answer is -283.