Q:

Drop terms of overall odd orders of multiple variables

I have the following expression:

a x + b y + c x^2 + d x y + e y^2 + f x y^2 + g x^2 y + h x^2 y^2 + i x^3 y^2 + 
   j x^2 y^3,

I would like to discard all terms of odd numbered combined orders -- such as i x^3 y^2 and f x y^2, but not d x y.
How do we do that? 

A:

Update: for the general case where some terms may contain only one of the variables x and y:
ClearAll[deleteOddOrderF]
deleteOddOrderF = Plus @@ Select[MonomialList[#], EvenQ[Total[Exponent[#, {x, y}]]] &] &;

deleteOddOrderF@expr

a x^2 + b x y + c y^2 + f x^2 y^2

deleteOddOrderF[expr + y^3 + x]

a x^2 + b x y + c y^2 + f x^2 y^2

Original answer:
expr = a*x^2 + b*x*y + e*x^2*y + c*y^2 + d*x*y^2 + f*x^2*y^2 + g*x^3*y^2 + h*x^2*y^3;

expr /. (x^a_.)   (y^b_.) /;  OddQ[a + b] :> 0

a x^2 + b x y + c y^2 + f x^2 y^2

