I hope I am able to do this. Because there are so many Pokemon that can learn Double Edge via the Move Tutor (and I'm not exaggerating -- 364 out of 386 of the Pokemon can learn it) I'm just gonna say all the Pokemon that can learn it from other methods. So basically every Pokemon on this list with about 22 exceptions can learn the move without the Move Tutor. Here we go:
Jigglypuff
Geodude
- Graveler
Golem
Onix
Cubone
Marowak
Chansey
Ledyba
Ledian
Togepi
Togetic
Marill
- Azumarill
Sudowoodo
Pineco
Forretress
Steelix
Phanpy
Blissey
Skitty
Aron
- Lairon
Aggron
Volbeat
Numel
Spinda
Chimecho
Relicanth
Bagon
- Shelgon
Salamence
Kyogre
Jirachi
I made this list with Excel, so excuse the spaces between the dot points.
Pokemon that can't learn it at all:
- Beldum
- Wynaut
- Cascoon
- Silcoon
- Wurmple
- Smeargle (he can Sketch though so)
- Wobbuffet
- Unown
- Ditto
- Magikarp
- Weezing
- Koffing
- Electrode
- Voltorb
- Haunter
- Gastly
- Muk
- Grimer
- Kakuna
- Weedle
- Metapod
- Caterpie
Hope I helped. :)
Source and Excel