There is an expression for the volume of a tetrahedron on the MathWorld site. Label the vertices of the tetrahedron 1, 2, 3 and 4, let dij be the length of the edge from vertex i to vertex j and let V be the volume of the tetrahedron then the MathWorld expression is the determinant equation
If you can find the height of the tetrahedron then you can use a much simpler expression.
volume = 1/3 (area of the base) height
The area of the base can be found using Heron's Formula.