Phenomenology is (i) an approach to philosophy and (ii) a philosophical tradition that has taken that approach. As an approach to philosophy, phenomenology is this idea: it pays philosophical dividends to describe experience as accurately and presuppositionlessly as possible. This approach was begun, at least in earnest or self-consciously, by Edmund Husserl – which takes us to the idea of phenomenology as a tradition or movement. The best known thinkers within that tradition are Husserl, Martin Heidegger, Jean-Paul Sartre, and Maurice Merleau-Ponty, although some other famous philosophers – notably Emmanuel Levinas and Jacques Derrida – sometimes get included in the phenomenological roster. For some detail on phenomenology and phenomenologists, one might see this article of mine.†
Like phenomenology, Critical Theory is both an approach to philosophy and a tradition of philosophers who have taken that approach. That said, the philosophers at issue – and some of the central figures here are Max Horkheimer, Theodor Adorno, Herbert Marcuse, Jürgen Habermas, and Axel Honneth – are not wholly or narrowly philosophers. For the idea of Critical Theory is this: philosophy’s point is that it can contribute to social theory, and, indeed, a form of social theory that shows what is wrong with the contemporary world and helps us to improve that world. For more, one may see here.‡
Moral philosophy is the branch of philosophy concerned with morality. Moral philosophy asks such questions as: How should I live?; What is the right way to act?; What does ‘right’ mean anyway? For a way into this vast subject, one might start here (although the sharp reader may ask why that article is entitled ‘Ethics’ as against moral philosophy; the glossary entry on ‘morality’ in my Philosophy and The Hitchhiker’s Guide to the Galaxy says something about that).
Metaphilosophy is the study of the nature – and point, and value – of philosophy. Hence one might say (although in fact this definition is controversial) that metaphilosophy is the philosophy of philosophy. There is more on metaphilosophy here (and in fact the link is to an article of mine to which some of the other links on this page point).
† I should perhaps add a third meaning of ‘phenomenology’. To wit: within so-called Analytical philosophy, the word ‘phenomenology’ denotes the business of describing what it is like to experience various things. Is that not the same as what Husserl and company are up to? Well, they do aim at such description, but they take themselves to be doing so in a rather strict (presuppositionless) way, and for philosophical stakes that are higher than most Analytical philosophers assign to the exercise in question. Members of the phenomenological tradition think that they can gain important insights into the nature of reality (and not just about the nature of experiencers) by describing experience. Reading about Husserl (say, here and here) may help one to appreciate this (philosophically controversial) point. For an exercise in actually doing phenomenology – phenomenology as Husserl and company understand it – see the Introduction to Cerbone’s excellent book Understanding Phenomenology.
‡ A caveat: some people use the phrase ‘Critical Theory’ differently. They use the phrase (or ‘critical theory’, i.e. without the capitalisation) to refer to work in literary and/or cultural theory that, while intending to be critical, often has little else in common with Critical Theory as I have used that latter notion. In the (relatively narrow) sense in which I am using the term, ‘Critical Theory’ is pretty much synonymous with another term that one encounters sometimes, namely, the term ‘the Frankfurt School’.