Bulbapedia says he learns it by event only. I don't have a Gengar so I can't try it.
No, Gengar cannot learn Sludge Wave through TM. The poison type moves it can learn through TM are Sludge Bomb, Toxic, Poison Jab, and Venoshock. Gengar can get Sludge Wave from the X/Y shiny Gengar event. Hope I helped! Source1 Source2
No it can't source: http://pokemondb.net/pokedex/gengar
