How to check whether the point is in the tetrahedron or not?

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For each plane of the tetrahedron, check if the point is on the same side as the remaining vertex:

bool SameSide(v1, v2, v3, v4, p)
{
    normal := cross(v2 - v1, v3 - v1)
    dotV4 := dot(normal, v4 - v1)
    dotP := dot(normal, p - v1)
    return Math.Sign(dotV4) == Math.Sign(dotP);
}

And you need to check this for each plane:

bool PointInTetrahedron(v1, v2, v3, v4, p)
{
    return SameSide(v1, v2, v3, v4, p) &&
           SameSide(v2, v3, v4, v1, p) &&
           SameSide(v3, v4, v1, v2, p) &&
           SameSide(v4, v1, v2, v3, p);               
}

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