In the Generation I Pokemon Games, there is unused trainer data for Professor Oak.
This would mean that, during some stage of the game a player was supposed to do battle against him.
In the trainer data mentioned, Oak has level 66 Tauros, level 67 Exeggutor, level 68 Arcanine, level 70 Gyarados and one of the Kanto starters at level 69.
This would mean that his strength is the same as the player's rival and the Pokémon League Champion. Four of his Pokémon are exactly the same as the ones used by the Champion, but at higher levels.
This means that he was originally meant to be Champion, or at least another high-ranking Trainer. In the game, there is an email on the PC in the Professor's lab that supports this. The email was sent by the Pokémon League wherein it issues a challenge to all Trainers and specifically asks Oak to pay them a visit.
The Professor is always at work in his Laboratory in Pallet Town where he is assisted by his aides. He is idolized by most Trainers and researchers, including Professor Elm.
Professor Oak mainly plays a supporting role in the games that he appears in.
In these games, him and Agatha were childhood friends and remained close friends until Oak stopped participating in battles and became a Pokémon researcher. The Professor still affiliates with the Pokémon League on an advisory level.