Cfrgtkky

I think the “until when” construct can work fine in a question like this, although I think I’d be inclined to change the order of the words:

I have until when to finish this project?

Also, it’s worth noting that we will often put additional emphasis on the word when in such questions, particularly when expressing surprise. For example:

Ted: I’ll need this project done by Friday.

Ned: I have until when to finish this project?

In this dialogue, Ned isn’t really asking Ted for a deadline; he is expressing incredulity that the deadline is coming so soon. In other words, Ned knows the project needs to be done by Friday, but he is astonished that he has so little time to accomplish so much work.

Of course, there are many other ways people can ask about an upcoming deadline. I especially like the suggestions provided by Bob Jarvis and Ronnie Childs elsewhere in answers and comments under this question:

• 
  When is the deadline for this project?


• How long do I have to finish this project?

There are certainly sentences where it would sound entirely appropriate.

Boss: Keep working on this.

Employee: Until when?

Parent: You are grounded!

Child: Until when?

Both usages are complete sentences. Used as part of a sentence sounds a bit more strained and unnatural.

Until when is occasionally used but not nearly as often as just when or by when.

So most common are:

When do I have to finish this project

and

By when do I have to finish this project.

But these two constructions don't necessarily mean the same thing.

The first is ambiguous; it can be understood either as at what time/on what day do I have to finish it - or by when do I have to finish it.

The second means by when must it be completed - by what time, day or other period.

People also ask:

What is the deadline for completion

So my recommendation is that you stick to: By when does it have to be completed.

Here is a related Ngram, comparing the use of by when and until when.

Until when is not a particularly common construct in this situation. You would be more likely to hear How long, as in:

How long do I have to finish this assignment?

Not a native, but I think natives would most commonly use

How much time do I have to finish this project?

However, I believe

Until when do I have to finish this project?

Might be grammatically sound. Now I am not entirely sure whether a native would use that or not

(Note: This is from a Northeastern U.S. native speaker's perspective.)

"Until when ..." is okay-ish, if a bit stilted. But "Until when do I have time ..." is just too clunky to be considered good colloquial English. See J.R.'s response for good ways to use "until when".

But this answer is to highlight what a previous comment pointed out: that the most natural way to say this would use the word "due":

When is the/this/our project due?

This is exactly how my students would ask me, multiple times throughout the semester.

Until when do I have time to finish this project?

I think there are two problems here:

• We don't need the word 'time' if we are using a preposition that relates the concept of time.


• 
  Until is a general word for something that is going to be happening, or true, for a certain time, and then stop being true (focusing on the period before the stop time). However, to focus on the deadline itself, we tend to use by (see Common Mistakes in Business English: The difference between “by” and “until”).

So we could say

By when do I have to finish this project?

...and if we aren't squeamish about finishing a sentence with a preposition, a UK speaker speaking informally might be likely to say:

When do I have to finish this project by?

To answer your title question though, "Until when" is perfectly natural for other cases:

"I'm working in the library."
"Until when?"

" 'Til lunchtime. I have to hand in this project by this afternoon"