Since pretty much none of these were covered in our Husserl episode as far as I recall, I thought this was worth my time to do some quick Wikipedia research and report back.
The phenomenological reduction, or epoché, is a suspension of judgments about the existence or non-existence of the external world. For Husserl, we are normally in the "natural attitude," which assumes metaphysical realism (as opposed to idealism), but he thinks that once we put aside that controversy, we can focus on the phenomena themselves. More generally, this is the phenomenological effort to stop shoving theories into our descriptions of experience, as, say, Hume pretty blatantly does when he states outright that our experience is all just impressions and ideas (which are really just faint impressions). It quickly becomes clear that this project of removing all theory from our descriptions is hopeless, but it's a move in the right direction, in that we want to figure out, at least, what theories are presupposed by experience, which leads to a whole study of language and the ego and all that.
Eidetic reduction is about analyzing essences: what makes the thing you're contemplating what it is. "This is done by theoretically changing different elements (while mentally observing whether or not the phenomenon changes) of a practical object to learn which characteristics are necessary for it to be it without being something else." In our Descartes episode, we brought up the example of the wax: he thought that since you can melt it and smash it, and it's still wax, then its shape wasn't part of the essence of waxiness.
Transcendental reduction, for Kant, is "examining experience in general and dissecting in it what is supplied by the mind from what is supplied by the given intuitions." To get at Husserl's definition (without actually wading back into the Cartesian Meditations, which I am loathe to do), this blog post quoting Steven Crowell in the Blackwell Companion to Phenomenology and Existentialism:
Husserl characterizes this as a reduction to “pure” consciousness, that is, to intentionality purified of all psychological, all “worldly” interpretations and described simply as it gives itself. What shows up in the natural attitude as simply there for me - the hammer I use, the rope I notice in the corner - now comes into view as a unity of meaning (a pure “phenomenon”) that is what it is precisely because of its place in the nexus of intentional acts and experiences in which it comes to givenness. The transcendental reduction thus allows phenomenology to study the intentional constitution of things - that is, the conditions that make possible not the existence of entities in the world (the issue of existence has been bracketed), but their sense as existing, and indeed their being given as anything at all.
All three of these moves are fair game for Husserl. I think by "essences" he has something particular in mind, which is not captured by Creeley's use of reduction to explain the analysis of theater performance. On a broader, more common-sense view of the term essence (which would have to, then, include musings like this too), you could certainly do such an analysis, but it's unclear to me what ones insight on Husserl would be contributing to the project then.