Question

Which Pokemon can learn Disable, Taunt, Torment, and Encore?

Answer 1

As of Generation IX:

/nds Disable, Taunt, Torment, Encore, all:
Alakazam, Banette, Chimecho, Drowzee, Gallade, Gardevoir, Gengar, Haunter, Hypno, Kadabra, Kirlia, Ralts, Sableye, Salazzle, Shuppet, Smeargle

Showdown commands

Answer 2

Alakazam, Gardeoir and Gallade are the only Pokemon to learn those moves.
Source: http://pokemondb.net/tools/moveset-search

Comments

Is that new tool?

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It's been around a few months I think. You find it under the Game Mechanics tab.