In Generation II, Bill's grandfather asks the player to bring him a "round, green" Pokémon with leaves growing on its head, referring to Oddish. However, in those games and subsequent generations, Oddish's body (unless it is Shiny) is blue. The mistake might have been a translation error caused by the ambiguity of the Japanese word aoi, which can mean both blue and green. This is fixed in Pokémon HeartGold and SoulSilver.
Oddish has a scientific name: Oddium Wanderus, given in its FireRed and Y Pokédex entries. The only other Pokémon with a known scientific name is Kabutops, with Kabutops Maximis.
Oddish's alias name is アルキメンデス Arukimendesu, as stated in the Japanese versions of FireRed as well as its Red and Green Pokédex entries. This can either be seen as a corruption of Archimedes, the Greek mathematician, or as a direct reference to a popular Japanese instant noodles brand Archimendes that literally means instant noodles on the go. The latter may reference Oddish's appearance when walking.
Oddish can be seen as a parallel to Bellsprout. Both are Grass/Poison-type Generation I Pokémon, part of a three-stage evolutionary line, can evolve starting at level 21, and whose second evolutionary event utilizes a Leaf Stone. Oddish is exclusive to Pokémon Red and FireRed, while Bellsprout is exclusive to Blue and LeafGreen, with both Pokémon found in the same locations in their respective versions. Additionally, both can be found at White Forest in White, and both Pokémon have had their Egg designs revealed.
In Pokémon Gold and Silver, Oddish is programmed to be able to learn Charm through breeding, but no other Pokémon in the Grass Group can legitimately learn it to pass down as an Egg Move in those games. In Generation III and IV, Oddish can inherit the move from Shroomish by chain breeding. In Generation V on, Oddish can inherit the move directly from Cottonee.