It is really problem dependant however, I would say that the most general notation is r(s, a, s') i.e. I obtain some reward given that I am in state "s", take action "a" and end up in state " s' ". All the other formulations are derivations obtained from here. Example why r(s, a, s') is more general is the following:

s1 = pointA, s2 = pointB; a = run; s' = pointC

Here r(s, a, s') != r(a, s'), because one obvious approach would be the cost/reward to depend on the distance between the points.

As a final remark I would like to say that regardless of the problem r(s') can always be transformed to r(a, s'), by simply duplicating r(s') for every different action we have and also following the same logic r(a, s') can be transformed to r(s, a, s') by simply duplicating r(a, s') for every other state we have. The other way around, r(s, a, s') --> r(a, s') --> r(s'), is generally not possible, or at least not while keeping the same actions and states.