しかも is pretty straight forward:

> 今度、「一番」ってお店のランチに行こうよ。あそこ、すごくおいしんだよ。 **しかも** 量もおおいよ。  
>  Let's go get lunch at Ichiban next time. The food is great, also the
> servings are big.
>
> うちの子は天才だよ。ピアノを弾くのが上手だ。 **しかも** 先月、英検２級を取った。  
>  My kid is a genius. He's great at playing the piano. What's more, last
> month he passed the 2nd grade of the Eiken.

I think of しかも as 'Also', 'What's more', or 'On top of that'.

The thing is I don't see how that is more different than それどころか. For example:

> この間食堂で食べた親子丼はひどかった。まず、にくはちゃんと焼いてなかったし、 **それどころか** ごはんは少なかった。  
>  I had a oyako-don at the dining hall and it was terrible. To begin with,
> the meat wasn't cooked properly, what's more, there wasn't a lot of rice.

I have a feeling that the translation of the two phrases is not going to
change very much when put into English, but that is not really important. What
I want to know is the correct time to use each respective phrase. Or, are they
not as interchangeable as I am thinking?

Thanks!
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usage word-choice set-phrases
What is the difference between しかも and それどころか?
I think that しかも simply emphasizes what follows, whereas それどころか suggests a
nuance like "and, as if that wasn't enough already ...". In your example

> 肉はちゃんと焼いてなかったし、しかもごはんは少なかった。  
>  The meat wasn't cooked properly and, what's more, there was only very
> little rice.
>
> 肉はちゃんと焼いてなかったし、それどころかごはんは少なかった。  
>  The meat wasn't cooked properly and, as if that wasn't bad enough, there
> wasn't enough rice (to go with it).

The version with しかも emphasizes several facts which amount to the 親子丼
experience to have been awful.

The version with それどころか suggests that the badly cooked meat alone would have
made the experience awful, but on top of that, there wasn't even enough rice.
I think the second sentence is a much more serious criticism of the
restaurant.
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どちらも添加に変わりはありません。

しかも・・・２つの使われ方があり、１つは「前で述べた内容に同じ種類の句を付け加える」使われ方、もう１つは「前で述べた内容に別の種類の句を付け加えて前で述べた内容を修飾する」使われ方です。  
同じ添加の接続詞の「そのうえ」は若干強調したい時に使います。

それどころか・・・「それどころか」は、文と文を接続します。それは前の文の内容をさしています。  
「どころか」は語と語、句と句を接続します。  
前で述べた内容から相手が「予想できない」または「知らない」ような事実を付け加えるときに使われます。

ここに載ってます  
<http://pothos.main.jp/setuzokusi.htm>
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