Algorithm to find all acyclic orientations of a graph
As Yuval noted, you can count the number of acyclic orientations by evaluating the chromatic polynomial of a graph at negative unity. For computing chromatic polynomials, there are efficient algorithms known for some graph classes.

There is also a recursive algorithm for generating all acyclic orientations of a graph given by Squire [1]. The algorithm requires $O(n)$ time per acyclic orientation generated. Roughly 20 years ago this was the fastest algorithm known; it's possible a faster one is known now, or that you can improve Squire's algorithm by known techniques.



[1] Squire, M. B. (1998). Generating the acyclic orientations of a graph. Journal of Algorithms, 26(2), 275-290.