How to pronounce $\mathcal{E}$? How to say $\mathcal{E}$ when we are speaking about mathematics? Can I call it "curly E"? 
And also how to pronounce $\mathcal{A}$ and $\mathcal{B}$ and $\mathcal{P}$ and so on?
 A: A useful resource for "speaking" mathematics is The Handbook for Spoken Mathematics by Lawrence A. Chang.  This book suggests that we should use a description of the font or script, plus the name of the letter (see pages 3–5).  Hence $\mathcal{E}$ might be read as "calligraphic capital $E$".  In most contexts, this would likely be overkill and require too much talking—I gather that much of the intent of the Handbook is to give a guide for instructors of blind students.  Hence an abbreviated "calligraphic E" might also be appropriate, as we can rely on students to read / copy what is on the board in most circumstances.
Other thoughts (including those above):

*

*Follow the handbook:  "calligraphic capital [letter]" or "calligraphic [letter]".

*Describe the letter more loosely: "script [letter]", "curly [letter]", or "cursive [letter]".

*Use TeX:  "mathcal [letter]" or "cal [letter]".[1]

*Don't Sweat It: "[letter]".[2]

*Name the Symbol from Context: as suggested in this answer, the symbols may have specific meaning in a given context.  For example, $\mathcal{H}$ is "the Hilbert space H", and the symbols $\mathcal{X}$ and $\mathcal{Y}$ are "the Banach spaces $X$ and $Y$".


[1] This is what I find myself doing most often.  The symbol $\mathscr{H}$ is "math script H", while $\mathfrak A$ is "mathfrak A".  This sometimes causes me problems in classrooms where I am dealing with students who don't know TeX, but has never been an issue when talking with my peers.
[2] This option will often be the most appropriate.  For example, the space of distributions $\mathcal{E}'$ is just "E prime".  There may be potential for ambiguity, but in many, many contexts, it just won't be a problem.  I mean, do we often make a big deal about an element $x$ in a space $X$?  Sometimes we carefully speak the letters out loud, but I find myself saying "Let eks be an element of eks..." more often than I care to admit.
A: It depends on your audience and the context. In physics, $\mathcal E$ usually denotes emf, so you would say that. In set theory, $\mathcal P$ usually denotes a power set, so you would say that. Otherwise, just do your best to describe it in a manner that your audience would understand. “Curly” or “calligraphic” works fine in my opinion.
Side note: You actually can type $\mathcal E$ into Google if you use the Unicode character ℰ (U+2130).
