How to ask this question correctly?
Is there any volunteers? or
Are there any volunteers?
It is enough to get at least one volunteer to do the job, but it is also good to get more volunteers.
Your choice of word must agree with "volunteers", so it has to be "are".
If you want one volunteer, you can say "Is there a volunteer?" (or the more idiomatic, "Can I have a volunteer?").
There is no simple construct that implies "I will accept one but would like more". You would have to say that explicitly. e.g. "Can I have a volunteer? Preferably more than one..."
Another way to do this would be, "Are there one or more volunteers?" But in this case, you really could argue about whether "is" or "are" is correct! (Does it agree with "one"? Or with "more" and "volunteers"?)