For each set of heads speaking, all three heads are actually describing the same thing, which is one letter from the alphabet. The letters are as follows:
Head 1: It's a common mathematical constant!
Head 2: No, it's like a currency symbol!
Head 3: No, it's like a set theory symbol!
This gives E, as in Euler's constant, the Euro, and ∈.
Head 2: It's associated with correctness!
Head 1: No, it's associated with time complexity!
Head 3: No, it's associated with nothing!
This gives O, as in a circle (as opposed to a cross), Big O notation, and zero.
Head 3: It's the sound in symbol!
Head 2: No, it's the sound in wash!
Head 1: No, it's the sound in king!
This gives C, as in the 3 sounds it commonly makes in words: /s/, /sh/, and /k/.
Head 3: It's me!
Head 1: No, it's an element!
Head 2: No, it's imaginary!
This gives I, as in myself, iodine, and the square root of negative 1.
Head 2: It's a drink usually served hot!
Head 3: No, it's a piece of golf equipment!
Head 1: No, it's a light afternoon snack!
This gives T, as in tea, tee, and tea.
Head 1: It's a number!
Head 3: No, it's a variable!
Head 2: No, it's an unknown!
This gives X, as in the Roman X for 10, the variable x, and the concept of X being used to represent the unknown.
Each of the different permutations the heads can speak in is represented here. Rearranging the letters so that they speak in the orders 123, 132, 213, 231, 312 and 321 gives the final answer EXOTIC.