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,
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,
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).
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).
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.