The minimum set of axes you need to test are all those at right angles to the faces of the polyhedra. If none of these have an overlap the shapes are disjoint.

To get a left hand right angle vector for x, y, you simply use -y, x.

[EDIT - bit more info now not on phone :)]

Assuming 2D here, you can loop through each shape and construct a vector from each vertex to the next one (B - A, C - B etc where the vertices are in A, B, C... order). If you then do the -y, x trick you end up with vectors pointing outwards at right angles from each face. These vectors represent the axes you need to test by projecting the vertices of each shape onto them and then comparing the min-max of each projection to see if they overlap.

You can ignore any axes that are equivalent to those that are already being tested, including any that point in the exact opposite direction as well as those which point in the same direction. It is common to precalculate these axes so you can trim out these duplicates as a post-processing step.

Let's see if a picture helps.

The red lines are the normals of each of the faces of the shapes, so in this case you have the three for the triangle and the two red for the square. You should be able to understand that the two green lines are not also required as they are directly opposite the existing red lines for the square.

So the set of axes to test is the total set of face normals of the two shapes, less any that are the same as or directly opposite the ones already being tested. It can be proven mathematically by more clever bods than I that if these axes are all without overlap, there exist no axes with an overlap therefore the shapes are disjoint.