For me all of them have a different purpose. By default, if you want sequential code: Async/Await. More readable.
If you are in an event driven code (with a trigger that can be called several time), you have to use callbacks.
In some very specific cases, I use promises, for instance to have a queue of operation

I use promised more out of not being fully comfortable with async/await yet, even though async/await seems like the better tool for the job in a lot of cases. But I always hated callbacks, so anything else is better. 😄

async-await - but sometimes it just makes sense to use a then with a traditional Promise.
We should remember that async is nothing but a 'wrapper' or syntacic sugar for a Promise - it's not wholly different thing.
async just makes our code a bit easier to read as it 'looks' 👀 synchronous. And, no callback is needed, mostly. 👍🏾
Callbacks are generally just for 'event based' UI stuff, such as addEventListener.

Callbacks always leads to callback hell. If I start something and end up needing more than 3-4 asynchronous calls, I will always refactor to async/await if for some reason I start up with callbacks (it happens, particularly if I start from an example).

I actually jumped from callbacks to async/await. Promises for some unknown reason just didnt capture the "full fix" to the problem for me. I had battled callbacks for a long time and I think smaller, cleaner functions ended up reducing the amount of callback hell I hit in a single implementation. I started to notice posts on various blogs discussing the endless .then world too.

In the end when async/await came along it felt like the most natural method to writing code, without the nesting and ultimately more readable.

Async await when there are multiple async actions, but I don't mind using callbacks for simple stuff like running a function after 2 seconds seconds using useTimeout.

Well, Promises and Async/Await are basically the same, so I use both of them but I don't use callbacks because I don't like them.

RxJS, Async/Await, Promises, callback functions. This is my list of tools composed by preference priority.

I prefer to use Async/Await.

Why?

It feels more natural to handle asynchronous calls in this way. It also saves me from having a nested structure which sometimes happens when using callbacks. And I think that Async/Await uses a cleaner syntax than the other implementations. It makes async calls look more like synchronous javascript, so it's easier to understand.

So, that's why I am a big fan of the Async/Await way of handling async calls! ❤