Here are gastly's learnable moves in the current (4th) generation.
By level:
start - Hypnosis
start - Lick
5 - Mean Look
8 - Spite
12 - Cures
15 - Night Shade
19 - Confuse Ray
22 - Sucker Punch
26 - Payback
29 - Shadow Ball
33 - Dream Eater
36 - Dark Pulse
40 - Destiny Bond
43 - Nightmare
By TM:
06 - Toxic
10 - Hidden Power
11 - Sunny Day
12 - Taunt
17 - Protect
18 - Rain Dance
19 - Giga Drain
21 - Frustration
24 - Thunderbolt
27 - Return
29 - Psychic
30 - Shadow Ball
32 - Double Team
36 - Sludge Bomb
41 - Torment
42 - Facade
43 - Secret Power
44 - Rest
45 - Attract
46 - Thief
48 - Skill Swap
49 - Snatch
53 - Energy Ball
58 - Endure
61 - Will-o-Wisp
63 - Embargo
64 - Explosion
66 - Payback
77 - Psych Up
78 - Captivate
79 - Dark Pulse
82 - Sleep Talk
83 - Natural Gift
85 - Dream Eater
87 - Swagger
90 - Substitute
92 - Trick Room
By Move Tutor:
Fire Punch
Ice Punch
Icy Wind
Knock Off
Ominous Wind
Sucker Punch
Trick
Thunderpunch
Snore
Spite
Uproar
Pain Split
Egg moves:
Psywave
Perish Song
Haze
Astonish
Will-o-Wisp
Grudge
Explosion
Fire Punch
Ice Punch
Thunderpunch
Disable
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No, Gastly cannot learn to fly.
No Gastly cannot learn fly in Pokémon HeartGold.
Gastly learns Mean Look on level 13.
Yes gastly learns mean look when he envovles to haunter
u cant but gastly knows it and golbat learn it after a while aswell u catch gastly in the dim cave on the pokewalker