Never mind the fact that different religions have different ideas of a deity and the supernatural; an irrelevant observation. Do Christians agree even amongst themselves on how to define God?
First of all, this is a type of fallacy where someone's inability to know something is automatically equated as that something being wrong simply out of some kind of presumed "embarrassment" on the part of the accused. Since this relates to all religious people personally, and it's presumed that religion is dead without the ability to define something within it, this can sort of fly by here.
But is someone's inability to label something some kind of indication of inconsistency in his ideology or its adherence? Can anyone who has ridden a bike describe exactly how to do it outside of showing someone the experience? If someone doesn't know how to explain how a car works, does it mean they can't be a good driver? This is the fundamental point behind the Sorites Paradox: no one can even really give a definition of how many grains "officially" form a pile of sand, nor does one need to.
Of course, the assumption is that if two different people can't agree on something as basic and fundamental as a definition of God, then that's supposed to mean they follow vague generalizations and don't really know what they're talking about. Of course, when one asks what an atheist adheres to with respect to religion, his answer is a simple negative along the lines of, "I reject all belief in the supernatural." Dig a little deeper and ask two different atheists what "the supernatural" or "God" are, and you'll see the same dilemma. A more clever answer would be that one doesn't have to define the non-existence of something and one's personal lack of belief in it. Of course, this evasion is not only intellectually dishonest, but inconsistent itself, because you can't deny something that's unknown or undefined to you with any reasonable certainty if the theist isn't allowed to have the same freedom of a general idea as we showed with the car example. You can know a truth about a concept without knowing its specifics. For example, I know that I don't know everything: I'm aware of the existence of physics, chemistry, and biology and what they're about, but I don't know everything in them.
One is reminded of the scene with Jack Nicholson and Adam Sandler in Anger Management where Nicholson's character repeatedly asks Sandler, "Who are you?" After several attempts to describe his background, job, etc, Nicholson continuously interrupts with corrections like, "I'm not interested in your origin, or what you do. Just tell us...who you are." When Sandler attempts to look for an example by asking what others answered, he's mocked with, "You want him to tell you who you are?" The point is, often, especially with an infinite and in many ways mysterious God, the best definition is by what He does and how one interprets His actions.
Moreover, different people will describe the same thing in different terms, be it God, or something no one can deny such as friendship, truth, and any other non-corporeal idea or reality. That's why the little cartoon, "Love is..." can have hundreds of different answers.
Secular, Scientific, and Technical Examples of Non-Definition Today
But just to be thorough, I'll give a few examples from technical, modern, and scientific sources. For example, what is the definition of mathematics? From the Wikipedia article on Mathematics:
Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. [Cajori, Florian (1893). A History of Mathematics. American Mathematical Society (1991 reprint). pp. 285–86. ISBN 0-8218-2102-4.] Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. [Mura, Roberta (Dec 1993). "Images of Mathematics Held by University Teachers of Mathematical Sciences". Educational Studies in Mathematics. 25 (4): 375–385.] There is not even consensus on whether mathematics is an art or a science. [Tobies, Renate & Helmut Neunzert (2012). Iris Runge: A Life at the Crossroads of Mathematics, Science, and Industry. Springer. p. 9. ISBN 3-0348-0229-3. [I]t is first necessary to ask what is meant by mathematics in general. Illustrious scholars have debated this matter until they were blue in the face, and yet no consensus has been reached about whether mathematics is a natural science, a branch of the humanities, or an art form.] A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. [Mura, ibid.] Some just say, "Mathematics is what mathematicians do." [Mura, ibid.]
If mathematicians can't even agree on a definition of their field, does it mean mathematics is a fictional waste? If mathematics is even undefinable according to some mathematicians, does it make them or the field inconsistent? Many more examples can be given for much more concrete and less debatable regarding a definition subjects. For example, the U.S. dollar:
Various acts have subsequently been passed affecting the amount and type of metal in U.S. coins, so that today there is no legal definition of the term "dollar" to be found in U.S. statute. [Yeoman, RS. A Guide Book of United States Coins]
There is still modern uncertainty as to which is the longest tributary of the Kagera River, the longest feeder of the Nile. The bottom line is that this kind of legalism isn't a prerequisite for being a consistent believer, and the difference between knowledge and action is exactly the type of loophole that James deals with in James 2:14-26 (particularly vv. 16, 19).
In conclusion, the inability or "inconsistency" in defining something, be it God, morality (such as a list of commands that my conscience obeys that yours must too!), or whatever, does not equate to a negation of its truth or validity - not even to a higher chance of this if this is all that's looked at (versus, e.g., an undefined location for a supposed treasure - it's a higher chance it's a myth with such fewer details). One cannot "positively" define something without relating it to something else he knows but hasn't defined, and this argument is simply circular and devoid of any information or meaning. It would be like asking what "space" is and arguing that Zeno's Paradox of Space implies it is undefinable and meaningless/nonexistent. Defining a "spirit" as a non-corporeal entity, therefore, does not make it a "non-definition" (i.e. what it is not) in any meaningful sense, nor does it negate its existence simply because it's outside of our reality (hence if "something" and "everything" is in our universe, "anything" outside it is "nothing" and a construct of our imagination). Something the consensus on Quantum Mechanics' Multiple World Interpretation itself would disagree with.