What particle to use after ほか

Question

I don't understand how to use the right particle after ほか.

Are these examples correct? If yes, what are the differences or nuances between these examples?

What else did you eat? :

• ほかに何を食べましたか。
• ほか何を食べましたか。
• ほかには何を食べましたか。

I didn't eat anything besides pizza.

• ピザのほかに何も食べませんでした。
• ピザのほかは何も食べませんでした。
• ピザのほかには何も食べませんでした。

Answer 1

Yes, your six examples sentences are all correct.

ほか followed by no particle works as a conjunction. ほかの works attributively (i.e., modifies the following noun). This difference is important:

• ほか、牛がいる。
  In addition, there is a cow. / Besides, there are (some) cows.
• 猫のほか、牛がいる。
  In addition to the cat(s), there is a cow.
• ほかの牛がいる。
  There is another cow. / There are other cows.
• × 猫のほかの牛がいる。 (nonsense: "cows other than cats")

ほかに is tricky and it can work like both ほか and ほかの. There tends to be a small pause or a comma when it works as a conjunction.

は in your examples is just a topic/contrast marker, and it's often optional (see this and this for similar examples). It's particularly common in negative sentences. It adds a slight emphasis, but doesn't change the overall meaning of the sentence.

Answer 2

The difference is very subtle, and I don't think using ほかに/は/には gives much nuance by themselves. It is rather that using one might be more natural than others due to the emphasis put by は.

Suppose Alice is asking Bob for the list of things he ate. Alice already knows he ate pizza.

• ほかに何を食べましたか？ is neutral, just asking anything else he ate.
• ほかは何を食べましたか？ sounds like Alice knowing that Bob must have eaten something other than pizza.
• ほかには何を食べましたか？ sounds the same as ほかは.

As an answer in the situation above,

• ピザのほかは何も食べませんでした。
• ピザのほかには何も食べませんでした。

sound (slightly) more natural due to は of contrast. To think in the opposite direction, the presence of は suggests Bob knows Alice knows that he ate pizza.

In a different situation where Bob was just found barely surviving in a snow mountain, and Alice asks did you eat anything?, then as Bob's answer,

• チョコレートひとかけのほかに何も食べてません

would sound more natural because は in the others emphasize that he did eat something (a piece of chocolate), which is not really important in the given situation.

Note that these are a bit artificial, and the uses are not really exclusive (actually likely to be interchangeable in most cases).

[Edit]

I came up with an example where only ほかは is acceptable. But again, this is not about nuance but the grammatical function of は (or of absence of に).

Suppose Alice is checking Bob's composition. She has pointed out several mistakes, and in order to say the rest is fine, Alice can use only

• ほかはOKです.

ほかには or ほかに cannot replace the ほかは above. This would be because (1) に means an addition to the previously mentioned (mistakes in this case) and (2) は indicates a subject.

On the other hand, to say there is no other mistake, all three can be used (phrases in parentheses are implicit).

• ほかに（間違いは）ありません
• ほか（の間違い）はありません
• ほかには（間違いは）ありません

The first (ほかに) might sound a little strange but should be understood. Note a comment in naruto's answer that は is frequent in negative sentences.