Dragon type moves are only super-effective against other dragon Pokemon. However, if the dragon type move is on a dragon-type Pokemon, the move will do substantial damage to many different Pokemon. This is because, dragon-type Pokemon usually have outstanding stats which make them stronger than other Pokemon.
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They are supereffectively strong only against other dragon type pokemon. Other than that, they are very strong moves that do a great deal of damage to other types of pokemon.
Dragon type moves are only strong against dragon type Pokemon.
Dragon-Type moves are only strong against other Dragon-Types. Dragon-Type Pokémon are strong against Fire-Types, Water-Types, Electric-Types, and Grass-Types.
Ice types are supereffective and so are dragon types. Yes, dragon types ARE EFFECTIVE against dragon types. In some dual-type dragon pokemon, like Garchomp for example, Ice is 4x effective to it and Dragon types, 2x
Dragon Pokemon are weak to ice and dragon type moves, and resistant to electric, fire, grass, and water type moves (By resistant I mean that when those type moves hit a dragon Pokemon, they will only do half the damage that they normally would). (This answer only applies to pure dragon Pokemon. Extra types such as flying/dragon, will have more weaknesses and strengths.)
A Dark Dragon Pokemon takes double damage from Fighting, Ice, Bug and Dragon moves.