goku probably became ssj3 in the other world but in his own time while no one was around
Episode 230 "Super Saiyan 3"
Goku does not turn super saiyan 6 or 5 in fact. and it only goes up to super saiyan 3 in the manga and super saiyan 4 in the cartoon.
Yes each super saiyan stage is stronger than the previous for example super saiyan 2 goku is stronger than super saiyan goku although the second stage is slower than the first stage power wise it's an improvement super siayan 3 is stronger than 2 and faster as well super saiyan 4 goku is the fastest super saiyan form (of goku only not counting fusion with vegeta) and is the last duper saiyan stage goku reaches.
Majin Goku
goku ssj 3
super saiyan 3 goku, have u even seen his flowing golden mane and blue eyes?
Goku had been training hard in other world, during this time he had achieved Super Saiyan 3 however, due to the differences in the areas, the super saiyan three goku had been able to do in other world, was a lot harder and drained more energy on earth. Vegeta, did not have his body at this time period, and thus was unable to train.
230. Super Saiyan 3?! no it's episode 245 because i just watched it
Goku goes super saiyan 3 episode 246 in dragon ball z the episode name is super saiyan 3?! So its kinda hard to miss
Broly the legendary super saiyan 3
Super Saiyan 3?!
He trains for a number of years in the Other World after being killed by Cell and learns Super Saiyan 3 during this time period.