The level requirements in order to a traded Pokemon to obey you differs from game-to-game. But beating the 8th gym make all traded Pokemons to obey you.
In RBY and FRLG,
Cerulean City gym: lvl 30
Celadon City gym: lvl 50
Saffron City gym: lvl 70
Viridian City gym: lvl 100
In Johto games,
Violet City gym: lvl 20
Azalea City gym: lvl 30
Ecruteak City gym: lvl 50
Cinnabar Town gym (GSC): lvl 70
Olivine City gym (HGSS): lvl 70
Blackthorn City gym: lvl 100
In RSE,
Dewford Town gym: lvl 30
Lavaridge City gym: lvl 50
Fortree City gym: lvl 70
Sootopolis City gym: lvl 100
In Sinnoh Games:
2 Badges: lvl 30
4 Badges: lvl 50
6 Badges: lvl 70
8 Badges: lvl 100
In Unova games, ORAS, and LGPE,
1 badge: lvl 20
2 badges: lvl 30
3 badges: lvl 40
4 badges: lvl 50
5 badges: lvl 60
6 badges: lvl 70
7 badges: lvl 80
8 badges: lvl 100
In Kalos and Galar games,
1st badge: lvl 30
2nd badge: lvl 40
3rd badge: lvl 50
4th badge: lvl 60
5th badge: lvl 70
6th badge: lvl 80
7th badge: lvl 90
8th badge: lvl 100
Source
Hope this helps :)
