Legal body means body legalised by the authority, like as a firm gets legal body after registration.
Constitutional body that kind of body which are framed in constitution through founder of constitution like as election commission, u.p.s.c, c.a.g and so own.
Statutory body means which is framed by the parliment through passing a statute, like as c.b.i and so own.
The planning commission is not a constitutional body and neighter it is a statutory body, it is from the british time, but we can say it extra constitutional body.