They are removed when you beat the Elite Four and become champion.
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it will only move if you have pokemon black or pokemon white.
Actually to teach this move to Gengar you need to find the move tutor that will teach the move to any of your Pokemon this move tutor is in Viridian city you need the HM Cut to get to him though. Also a move tutor in Pokemon xd gale of darkness will teach Dream Eater to your Pokemon.
With the HM move strength.
Find the move deleter.
He is in Mistralton City in the house next to the pokemon center