A plane divides the 3D space in two regions, and if you have several planes, in general you cannot say wich one of the halves is inside or outside. You have to select which side of the plane will be inside and them make a selection (iterating with each plane) and discarding the points that lie outside this new plane. A good method to discern is to apply the plane equation to the point and see if it yields negative or positive result:
Ax + By + Cz + D = 0
is the equation of a plane in 3D, so if you put the point coordinates you'll get a positive, zero or negative number (if zero, te point belongs to the plane and so, it's neither inside nor outside of the region)
for a tetraedron (just four planes) you can have only one bounded region (or even none, in case the four planes coincide in one point), but you have 15 more unbounded ones. In case of five or more planes, you can have more than one bounded region, so you cannot apply the bounded property to consider being inside.
I think the most practical thing (instead of searching all possibilities, as the number of regions grow exponentially with the number of planes) is to consider which side of the plane makes the points to be inside or outside of your region, and apply the plane function to them to see if they are inside or outside.
Another issue to consider is what you define the region inside, as I'm supposing you mean being at one side to be inside and being inside only if all planes agree (this deals you to a convex polyedron) but the definition can be modified to only some of them, to consider nonconvex, bounded regions or several other criterion...
I expect this explanation gives you some light on the subject.