Philosophers certainly use these categories frequently in their discourse, and in fact, in one metaphilosophical theory, wisdom is the primary goal of philosophy, sometimes called "philosophy with the big P". I suspect most professional philosophers would agree with the claim that wisdom is either a necessary or sufficient condition for eudaimonia. But there are no standard set of philosophical precising definitions that define each. Definitions from the OED is as likely as you'll get to some sort of standardization of these words.
It is arguable that the basic unit of philosophical discourse is the proposition. At least in the analytical tradition, heavy emphasis is placed on truth-conditional semantics, and much ink is spilled over proving or denying the veracity of claims. There is God. There isn't God. Numbers are real. Numbers aren't real. We are more than our bodies. We are not more than our bodies. And the mind controls the body. The mind doesn't control the body. But in that process of discourse and truth evaluation, different philosophers make different sorts of claims. Enter the epistemologists and their passion for epistemic justification. There are beliefs, and then there are beliefs!
What was once just "some stuff people say" is now at a minimum recognized as belief, knowledge, and wisdom. Most philosophers dead or alive recognize these three categories as much as they may struggle over drawing boundaries. Both information and insights are words that hold some additional nuances of connotation. Of course, any epistemologist worth his salt is going to have a position on these five terms, and be capable of dueling with words to affirm their own knowledge (or mere belief depending on your personal views). Let's take a look at some uncontroversial statements about each.
Data vs. Information
Perhaps one of the simplest acts necessary for creating a taxonomy of knowledge is the act of dichotimization. Leibniz's Law comes to mind in such an act. It would uncontroversial among thinkers, I'd argue, that the data-information dichotomy is utilitarian practice when working with large swaths of representations (SEP), the philosophical term that might be used to subsume all of the categories you mention. In my own day to day existence, when I deal with data sets which might exceed millions of records with a hundred plus fields, it is useful to distinguish between raw data, sets of values mapped to a variable with sets of variables mapped to a table, and information. For instance, in an ICD code set, there are more encodings than, I suspect, most doctors are aware of. But, can I take those sorts of codes within the context of a task and do something practical and meaningful for them? Can I translate them into an EDIFACT data structure to send them to a hospital overseas? Hence, the raw material is a collection of codes, and the product is perhaps an insurance claim that a hospital in Norway might be able to use? Data and information.
Data, Belief, and Knowledge
Data and knowledge is an entirely different distinction. Any child might point to a computer, utter 'computer' and say, "I can read those words" of some text. But can a child understand the purpose of a set of healthcare records? Can they take those records in the spirit of big data and mine them for analytical conclusions? Of course not. It's questionable on some days if I can. Enter Ryle's distinctions of knowledge-how and knowledge-that. And this use of knowledge is different from the belief-knowledge distinction, which is arguably a more important distinction which begins to turn on the idea of justified, true belief. I may believe that a population of clients has a predisposition to cancer, but can I prove the claim? My knowledge of the veracity of a claim, therefore is paramount if I'm making practical, real-world choices. Vladimir Putin believed he could take Kyiv in 3 days, but did he know? In retrospect, obviously not!
Insights and Intuition
MW defines insight as:
1 : the power or act of seeing into a situation : penetration
2 : the act or result of apprehending the inner nature of things or of seeing intuitively
Talk about 'open to interpretation'! The 'inner nature of things'?!? 'Seeing into a situation'? Here is a recognition that not all propositions are created equal. The lay definition of an insight reflects the concepts that there is a deep, inner nature. I've always taken this to mean that intuitively philosophers are very much concerned with distinguishing the essential from the accidental (SEP), the necessary and sufficient, or perhaps distinguishing from among coincidence, correlation, and causation. All of these conceptual distinctions are important, because despite the protestations of the over-confident, human reason is highly normative and defeasible.
This is often touted as the best end to philosophy. While professional tribes of Continental and analytical philosophers often have very technical pursuits and rigorous conditions, taking philosophy back to Socrates, we can see there might be a higher purpose be it eudaimonia or Truth or salvation or satori or whatever you want to call it. In this vein, wisdom is about the teleological. Does life have meaning? How should I make decisions? What's the best way to do anything? Wisdom is often understood as a gradation of knowledge that has a normative aspect. Anyone can beat a dog into submission, but perhaps by whispering in his ear, one avoids getting bitten in the future. Albert Camus and his absurdism is a great example of contemporary philosophy that isn't technical at all. In fact, Camus espoused beliefs about rebelling against all of the language of philosophy and embracing a passionate, well-lived, personally meaningful life in the face of a naturalistic explanation of the universe. We see in Camus a sort of anti-philosophy.
Philosophy means many things to many people. Metaphysics has always been the art of selecting among "first-principles" and then interpreting the world. Having a consistent, meaningful, and useful taxonomy of propositions is one of the necessities of having a philosophically durable worldview. As we take basic units of meaning (morphemes, perhaps?) and build propositions, arguments, and theories from them, it helps to see how meaning itself can be identified with other practices, such as epistemic justification or teleological planning.