Measuring the randomness of CNF formulas
I suggest to borrow physics intuition that "less random" structures are more symmetric. Symmetry for CNF is any transformation of the variables, that keeps the function invariant. By that criteria, functions of 3 variables such as 

$\displaystyle x_{1} \vee x_{2} \vee x_{3} .$ 

or, say, 

$\displaystyle(x_{1} \vee x_{2} \vee \neg x_{3}) \wedge (x_{1} \vee \neg x_{2} \vee x_{3}) \wedge (\neg x_{1} \vee x_{2} \vee x_{3}) \wedge (\neg x_{1} \vee \neg x_{2} \vee \neg x_{3}).$ 

are less random than, say 

$\displaystyle(x_{1} \vee x_{2} \vee \neg x_{3}) \wedge (x_{1} \vee \neg x_{2} \vee x_{3}) \wedge (\neg x_{1} \vee \neg x_{2} \vee x_{3}) .$ 

In general, defining a concept of "random" on finite structures is challenging. Historically, it was tried on binary sequences, which arguably are the simplest finite structures. For example, intuitively, a sequence 01010101 is "less random" than, say, 01001110. However, it was quickly realized that there is no consistent formal definition of finite random sequence! Therefore, one have to be skeptical of any naive attempts to define a measure of randomness for any finite structure.